Phonemic vowel length occurs in widely across Uralic languages. This, however, is due to various independent developments — for long now, no vowel length is normally reconstructed in Proto-Uralic.
Quality distinctions are one common source of length. In particular PU *a and *ä yield long vowels unconditionally in several languages, such as across all of Samic and Ob-Ugric, as well as in Nenets. Other sources include compensatory lengthening and syllable contractions, both of which could be exemplified by Hungarian (but this is not today’s topic).
In Finnic, one major source of vowel length has been loss of medial segments: this includes developments such as *uwa > (? *ua >) *oo, and *ewə, *eŋə, *exə > (? *ew >) *öö. (Further loss of medial segments in connection to consonant gradation has created a later layer of long vowels in many of the languages; possibly most long vowels in modern Finnish fall in this group!) As I’ve mentioned before, apparent “primary” long vowels can also be found, which correspond to single vowels elsewhere in the Uralic family.
Previous explanations attempted, in another chapter of overreliance on Finnic in Uralic reconstruction, to explain these as being inherited from some older stage. A recently re-emerged theory due to Meri Lehtinen, however, examines the distribution of these cases and notes that not only are these restricted to *e-stems, they also almost entirely occur before sonorants: *m, *n, *l, *r and pre-Finnic *ð. Hence, she proposes vowel lengthening before resonant + *e (probably earlier *ə by this point).
Further elaboration on this model has been recently done by Aikio , who finds that this theory makes for a particularly good explanation in deriving the long mid vowels *oo and *ee (reflected as /uo/ and /ie/ in Finnish, Karelian & Livonian, but Standard Estonian and Votic /oo/, /ee/) from earlier, you may have guessed it, *a and *ä. As the change is specific to Finnic, PU *ë is also affected, via the West Uralic shift *ë > *a.
Not only is this sound law highly non-trivial, it also carries many interesting consequences. That no long vowels or any special conditioning segment *x need to be reconstructed for any stages preceding Finnic is only the most obvious one. Beyond this, I notice several further smaller effects of the theory. As such this might be one of the more important sound laws defining Finnic — and probably deserves a name. In the following discussion I’m going to call it “Lehtinen’s Law”, or “LL” for short.
Interestingly, *ŋ, the velar member of the nasal series, is absent from the consonants conditioning Lehtinen’s Law. (No good evidence exists on what effect the palatal nasal *ń might have had.) While perhaps the most typical reflex of *ŋ in Finnic is *v (*aŋa- > *ava- ‘to open’, *suŋə > *suvi ‘summer’), in the same context as LL, *ŋ is lost with long open vowels resulting (*päŋə > *pää ‘head’, *kaŋərə > *kaari ‘curve, bend’). The long vowels *aa, *ää created here clearly must have come about later than those from LL, which were raised to *oo, *ee. A good explanation seems to be that only a part of this process had occurred — the vocalization of *ŋ, but not yet compensatory lengthening. After all, the semivowels *j *w are not consistent conditioning segments for LL. 
Neither *j or *w is feasible as the actual intermediate though, given examples like *śawə > *savi ‘clay’ (not **saa), *täjə > *täi ‘tick’ (not **tää). I believe the best option is to consider an apparent detour: *ŋ > *x! PU *x is reflected essentially identically to *ŋ not only here (*mëxə > *maxə > *maa ‘land’, *jäxə- > *jää- ‘to stay’) but also in other environments (*mexə- > *möö- ‘to sell’, *peŋərä > *pöörä ‘wheel’; *joŋsə > *jousi ‘bow’, *nox-ta- > *nouta- ‘to fetch’). It seems *x should be phonetically analyzed as a velar unrounded glide [ɰ] by this point in the development of Finnic.
This sound change is, of course, a highly likely intermediate for the development *ŋ > *w (> *v) in the first place, but I don’t believe it has previously been recognized that this stage would have been phonemically significant.
I can think of further ramifications of (and further support to) this change, but those would be getting much deeper into the development of secondary vowel length in Finnic than is necessary here.
2. Vowel substitutions in Baltic loanswords
LL also appears to clarify some issues in how the Baltic non-close long vowels *oo, *aa, *ee (the last one may have phonetically been closer to Uralic [ää]) are rendered in loans into Finnic. A discussion in Kallio (2008)  notes two substitution types for each:
- *oo → *oo, *uu
- *aa → *a, *oo
- *ee → *ä, *ee
According to previous understanding, with *oo and *ee but no *aa and *ää inherited from a Pre-Finnic stage, the first substitutes here would have been the older stratum. To explain the second set with *uu, *oo, *ee, Kallio ends up assuming that these reflect a Baltic variety where the original vowels had been raised towards higher values. However, these can be explained rather more cleanly from the intermediate stage of LL, where lengthening to *aa, *ää had occurred but raising to *oo, *ee had not. Baltic *aa and *ää would have been substituted with the same on the Finnic side, and would have ended up raised together with the primary long vowels that had emerged in inherited words. Meanwhile, since *oo did not yet exist in Finnic, Baltic *oo could have been substituted by *uu. Granted, *uu must also have been an innovation in Finnic — see next section. Still, the direct substitution *oo → *oo seems likely to represent a newer layer.
As for *aa, *ää → *a, *ä, it remains possible to analyze this as a very early substitution. It can however also be dated to a period during which Finnic primary *aa, *ää had been raised to *oo, *ee, but no secondary *aa, *ää had yet been introduced. This is functionally the exact same stage of development that was previously assumed — but it can be now placed later in the relative chronology.
3. On non-close long vowels
Lehtinen’s Law does not explain the long close vowels *ii *uu *üü which also occur in the layer of primary long vowels in Proto-Finnic. The last one was highly rare and seems to be explainable in connection to the loss of palatalization. There is a slightly larger pool of evidence for the other two. Aikio briefly covers this topic, too, but ends up noting that the cognates in other Uralic languages are too heterogenous for any single source to lie behind these vowels.
It’s possible to expand the amount of available evidence though. The previously observed link between Finnic primary long vowels and *e-stems is satisfactorily explained by Lehtinen’s Law — and no such connection needs to hold for the long close vowels, if they have a different origin. Thus, there is no reason to exclude Proto-Finnic word roots with the vocalism *ii-a, *ii-ä, or *uu-a from comparison with the other Uralic languages (as has been sometimes done in the past, including in Aikio’s analysis). Examples still aren’t numerous, but at least two cases seem promising:
- Finnish piira ‘crop (of bird)’; cf. e.g. Mokša /pärma/ ‘id.’
- Finnish kuusama ‘honeysuckle’; cf. e.g. Udmurt /guzempu/ ‘id.’ (/pu/ ‘tree’)
*ii and *uu are also known to regularly correspond to Samic *i and *u. The origin of these vowels is, in the wake of LL, currently also left as an open question (as original short *i and *u > Samic *ë and *o). From Samic, too, items pointing to older *ii-A or *uu-a can be found, e.g:
- *imē ‘uncle’s wife’; cf. e.g. Khanty *iimii ‘grandmother’
- *čukčē ‘capercaillie’; cf. e.g. Mari /suzə/ ‘id.’
- *puvē- ‘to strangle’; cf. e.g. Mokša /pova-/ ‘id.’
While I have a few ideas brewing on how to proceed with some of these, my current point is purely methodological: if we wish to find an explanation for the origin of *ii and *uu as well, this type of data should not be excluded offhand from the analysis.
4. On the distribution of PU *x
Under the previous model (due to Janhunen) of the development of Finnic long vowels, a strange double role had to be assumed for PU *x. Intervocally, this would have yielded mostly regular consonantal reflexes, while as the first member of a consonant cluster, it would have been vocalized or lost in every single Uralic language. There had never been any demonstration of “medial *x” versus “coda *x” being in fact the same phoneme — and of course given LL, this gets resolved by zapping the assumed “coda *x” from existence.
This has the result of freeing up the phonotactic structure *-xC- for other uses. Before Janhunen no clusters along these lines have been consistently assumed, though such cases do seem to arise in Finnic at least, such as *ńoxə- → *nox-ta- > *nouta- ‘to fetch’ mentioned above. There are however some issues I think reconstructing clusters with a first member *x could be able to patch. (Do note that all that follows in this section is highly speculative.)
Some posts ago I noted Khanty apparently distinguishing medial *-k- and medial *-ɣ-. Original single *-k-, *-w-, *-x- yield *-ɣ-, but in clusters involving *k, there does not seem to emerge a clear pattern: there are cases such as *äktä- ‘to chop’ > Western Khanty *eewət-, but *ëkta- ‘to hang up smth’ > WKh *ïïxət-. Possibly words of the former type could be adjusted to involve original *x rather than *k, thus e.g. *äxtä-?
A word that seems particularly promising here is that for “rope”, found as *piks in Mordvinic, *püüɣət in Khanty, fiu in Hungarian. Sammallahti reconstructs *piksə for this.
An immediate issue is that Mordvinic CiC(C) is an “etymologically impossible” root shape: a monosyllabic noun indicates PU *-ə, but both *e-ə and *i-ə are regularly continued by Mordv. *e. If one of these had to be picked though, *e seems like the less irregular option, as *e-ä yields *i-ə. And more relevantly: a known exception environment is the position before *x. Here development to *i occurred even before *-ə: *mexə- > *mijə- ‘to sell’, *wexə- > *vijə- ‘to carry’ (not **mejə-, **vejə-). If we were to reconstruct, on the basis of Khanty *-ɣ-, PU *pexsə, then this soundlaw is capable of accounting for the vowel in the Mordvinic cognate. We only need to assume fortition *xs > *ks, which does not seem like a major assumption despite being required widely across Uralic. Clusters of fricative+sibilant are very rare cross-linguistically, and have a tendency to fortite: consider e.g. German sechs /sexs/ > /seks/; the development of ξ from Ancient Greek /kʰs/ to Modern Greek /ks/, even though normally /kʰ/ becomes /x/ (I notice Wiktionary even presents /xs/ as an intermediate here); and the developent of PIE *ks to Proto-Germanic *ks, even though *k normally becomes *x.
*e here would also appear to cover Khanty better: several examples such as *sewə- > *ɬii- ‘to eat’, *lewlə > *liil ‘soul’ exist, and I believe *üü here (as discussed recently under the post on *ü in Mansi, perhaps only in Eastern Khanty; this vowel is not treated distinctly from *ii in Western) originates from labialization before *ɣ. The parallel mid vowel change *eeɣ > *ööɣ is quite well known and phonetically this may have been a retraction detour: [iː eː] / _ɣ > [ɨː ɘː]; > [ʉː ɵː] > [yː øː]. Alternately this could suggest that Eastern /ɣ/ ~ Western /w/ goes back to Proto-Khanty *w, not *ɣ.
Another word in which in particular I suspect *ɣ in Khanty could go back to a PU cluster of a shape *-xC- is ‘to leave, depart’ (> Southern Khanty /tiiwət-/), usually reconstructed *läktə-. *-kt- would work as usual for Finnic *lähte-, Udmurt /lɨktɨ-/, etc. Mordvinic again does something else though. The word is reflected as Erzya /ĺivťe-/, Mokša /ĺiçťə-/. Two apparent irregularities are seen here: the vowel /i/, for which an explanation somewhat similar to the previous case might apply (though precedents on the development of *-äx- in Mordv. are lacking); and the Mokša cluster /çt/.
Some background for understanding what the latter signifies. The distinction between *k and *x does appear in Mordvinic, but only indirectly: *-k- yields *-j- or *-v- depending on the vowel harmony class, while *-x- yields only *-j-. The cluster *kt regularly yields *-ft-. Previously Mokša /-çt-/ has been explained as the reflex in front-vocalic words — I think this however runs into problems given *nüktä- > /ńefťə-/ ‘to pluck’, or the inherited verbalizer *-ktA- being reflected as only /-ftə-/, /-fťə-/. The other cases of Mokša /çt/ incidentally also do not inspire confidence in this being a regular development of inherited *kt. I am aware of Er. /pivťe-/ ~ Mk. /piçťə-/ ‘to churn’; and Er. /ťejťeŕ/ ~ Western Mk. /ɕťir/ (*ç > ɕ is regular in these dialects) ‘daughter’, an Indo-European loan. Cognates in Samic or anywhere eastward are absent for these two words, and in Finnic, an irregular *-tt- appears (though not in *läKtə-): *tüttär, *pettä- (> Fin. tytär, pettää). Altogether an Uralic pedigree seems unlikely.
So, although the developments in Erzya are different in each case, apparently pre-Mordvinic *x had a greater affinity to lenite to something palatal than *k. I thus wonder if we could reconstruct Proto-Mordvinic *xt behind Er. /vt/ ~ Mk. /çt/; and hence PU *läxtə- ‘to depart’. Perhaps similarly ‘daughter’ was originally adopted as Proto-Mordvinic *tüxtir rather than *tüktir for some reason, and whatever the origin of ‘to churn’ is, perhaps the original form was *pextä- rather than *pektä-? I cannot say for sure, but I certainly can brainstorm some ideas here.
 I alreddy linked this in the post on PU root structure, but to repeat in slightly more detail: Aikio, Ante (2012): On Finnic long vowels, Samoyed vowel sequences, and Proto-Uralic *x. In: Per Urales ad Orientem. Festskrift tillägnad Juha Janhunen på hans sextioårsdag den 12 februari 2012. Suomalais-Ugrilaisen Seuran Toimituksia 264.