From a Uralicist perspective, one thing that I find goes underappreciated in Indo-European studies is the extensive phonotactic complexity of most IE languages. Certain types of studies on PIE consonant clusters can be found these days in abundance, yes… but these mostly focus on the resolution of the most extreme things that the morphology of PIE, with its abundant zero-grade morphemes, can come up with: monstrosities like *HHR-, *CRH-, *RHC-, *-CHCR-. The fate of the more common, though still remarkable on a worldwide scale, consonant clusters like *bʰl-, *sp-, *tw-, *-zd-, *-ktj- appears to be considered basically trivial. (I am open for reading suggestions, though: IE studies is a big field and I expect I am still missing out on many specifics.)
Within Europe, at least the fate of simple two-consonant initial clusters really is at least mostly trivial, though. The Germanic and Balto-Slavic languages retain most PIE initial clusters fairly well, incidental changes in the individual consonants aside (as in *tw- > English thw-, Lithuanian tv-). Latin and Greek are not far behind, though they mostly get rid of *sR clusters (as in e.g. slime ~ līmus; snow ~ nix). We would have to look at Albanian and the more eastern languages (Armenian, modern Indo-Iranian) before seeing major cluster simplification or transformation trends. As for Celtic, Tocharian and Anatolian, I can’t say I have much of a handle on the big picture at all… which is one reason why a detailed overview of phonotactics issues in the IE languages, either from the perspective of particular classes of clusters or particular languages’ overall histories, would sound appealing to me.
To be fair, it’s not as if this kind of a thing has been done much in Uralic studies either. There have been a few phonotactic analyses of the cluster stock in various reconstructed proto-languages, though with naïvely synchronic methodology. From a more firmly diachronic angle, a few interesting topics that may require more detailed investigation could be
- the nearly complete cluster simplification trends in Permic, Hungarian and Enets, transforming the inherited *(C)V(C)CV root structure into roughly √(C)V(C)(V). To a lesser extent similar things happen also in e.g. Mari and Proto-Samoyedic.
- the rise of numerous complex clusters in Mordvinic, e.g. in initial position, Erzya kši ‘bread’, kšna ‘strap’, pśkiźems ‘to have diarrhea’, promo ‘gadfly’. This seems to run a bit too deep-set to be blamed just on late Russian influence: the first two are earlier Baltic or Balto-Slavic loanwords (~ Fi. kyrsä ‘loaf’, hihna ‘strap’), the last two native Uralic (~ Fi. paskoa ‘to shit’, paarma ‘gadfly’).
- the slightly less daunting but still strong expansion of consonant cluster complexity in Finnic (as I’ve briefly covered before) and Samic, probably mainly due to Indo-European loanwords.
But back to IE, for a few scattered observations.
At least one of the initial consonant clusters reconstructed for Proto-Indo-European is an exception of sorts to any retention tendencies, even from an European perspective. This is *sr-: the cluster is alien to most European languages today, even ones that may otherwise allow sibilant+/r/: English shr-, German schr- from earlier *skr-. (The Slavic languages do have newly created examples though, generated after syncope; e.g. Polish srebro ‘silver’ < *sьrebro.) Given the wide palette of word-initial clusters of the type CR- and even sTR- tolerated in IE languages, this is a notable hole in the system.
In Greek *sr- is simplified the usual way, through *s-aspiration, yielding word-initial ῥ- /rʰ/. Elsewhere, however, special developments seem to kick in.
Germanic and Balto-Slavic share here a non-trivial isogloss: *sr (of any position) is resolved by epenthesis of *t, generating correspondences such as stream, Latvian straume, Polish strumień ~ Greek ῥεῦμα (< *srew-m-os, *srew-m-eh₂). The change has however not reached standard Lithuanian, which still has e.g. sraumuo;  therefore showing that this is a relatively late diffused sound change, not a data point in favor of a Germano-Balto-Slavic proto-dialect. Perhaps even one that has been innovated multiple times in parallel: homorganic stop epenthesis in clusters of continuant+glide is commonplace after all (æmyrge > *emrə > ember in English surely requires no especial connection with hominem > *homre > hombre in Spanish), and while the phonetic development is less trivial here, the prior existence of *str- has probably helped to motivate *t-epenthesis.
This sound change likely also accounts for the intrusive -t- in ‘sister’ in Germanic (sister etc.) and the relevant parts of Balto-Slavic (OCS сестра, Old Prussian swestro, but again, Lithuanian sesuo; and as I’m looking these up, I am also learning that Latvian has apparently lost this word entirely!). This was probably generalized from the genitive, *swesrés or *susrés. Some degree of analogical support from the mother, father, brother, daughter group surely has played a part as well, but I would think the fact that this only occurs in languages that also show *sr > *str as a general sound change is not a coincidence.
This development also seems to have interesting interaction with the PIE syllabic consonants. Some time ago I ran across a small article by Krzysztof Witczak (1991), “Indo-European *sr̥C in Germanic“, which proposes that this epenthesis also took place before syllabic *r̥. The evidence is scarce but looks believable. Interestingly, this then demonstrates that at some point an actual syllabic [r̩] must have indeed occurred in Germanic (contra some of my earlier suspicions that some kind of an epenthetic schwa might have been hanging around all along in here).
Also, returning to ‘sister’: while I have no ready means to see if this checks out in the other older Germanic languages, Wiktionary actually gives a PGmc genitive *swesturz > Gothic swistrs, which looks more like pre-Gmc *swesr̥s.
Even more interestingly, there seems to be some evidence for similar business also in Baltic.
The word for ‘roe deer’ in Latv. and Lith. is stirna, corresponding to Slavic *sьrna. These look like derivatives from the ‘horn’ root, *ḱer(h₂)-, or in particular the derivative *ḱr̥(h₂)nos, as reflected also in e.g. Germanic horn. Derksen’s etymological dictionary of Baltic (2015) has no comment other than that “the anlaut is problematic”… I suspect however that the Baltic words could be explained by a development *šr̥ > *str̥, taking place before the breaking *r̥ > *ir.  This all will also have to be later than *ḱ > *š, but this is already assured to be quite early by the evidence of loanwords in Finnic.
On the other hand, there are more than enough other words, even derivatives from this same root, that show no such epenthesis, e.g. Old Prussian sirwis ‘roe deer’ < *šr̥wis (whence also Fi. hirvi ‘elk’); Latvian sirsenis, Lithuanian širšė ‘hornet’ < *šr̥Hšō (whence also Fi. herhiläinen). To get around this issue, we would probably need to assume either dialect mixture of some kind — as will be already required to explain why we have *t-epenthesis now showing up in Lithuanian also. An irregular shift from *šr̥nos to *sr̥nos might also work. (Or as long as I’m fucking around with relative chronology, even the regular shift of *š to *s in Latvian?)
This is moreover complicated by how all these words must be, to some degree, analogical anyway. The reason for this is “Weise’s Law”:  the neutralization of *Ḱr- and *Kʷr- as *Kr-, common to all Satem languages. We would again not expect this to distinguish between syllabic *r̥ and non-syllabic *r, and apparently the Sanskrit data indeed confirms this. Thus Balto-Slavic *šr̥nas and other such derivatives (including, from Sanskrit, śiraḥ ‘top’ < *ćr̥Has) would have to be assumed to get their palatal onset by analogy with the abundant other derivatives of *ḱer(h₂)-. So… another possibility is then that stirna is the earliest word where *ḱ > *š was restored in this way, followed by epenthesis, followed by the remaining cases of analogical *š-restoration.
Or maybe this is all barking down the wrong root entirely. Something that also looks worth further investigation is if the Baltic words for ‘roe deer’ might be actually rather cognate with German Stirn?
A different angle on getting rid of *sr- is exhibited in Italo-Celtic: > *θr- > fr-, reflected at least in Brythonic (e.g. Welsh ffrwd ‘stream’) and in Latin (the best examples seem to be word-medial and have an expected further development to -br-, e.g. crābrō < *kr̥Hsrō ‘hornet’). Irish has what looks like retained sr- (e.g. sruth ‘stream’). Schrijver proposes that this is a reversal from the *θr stage,  but given the situation in Baltic, I would not bet on it. Note that reversal in Lithuanian is clearly not possible, since inherited *str- remains. Again, it seems plausible that the first stages of the Goidelic/Brythonic split go far back enough that the latter could have still participated in common developments with Italic.
Irish also seems to have a general shift *st- > s- (ser ‘star’, sab ‘staff’, etc.), so actually even an earlier development of the Germanic-Balto-Slavic flavor is theoretically possible.
A quick scan-over of IE etymological sources at my disposal reveals no special developments of *sr̥- in Celtic or Latin. LIV has two Latin examples that seem to have retained s-: sariō ‘I hoe’ < *sr̥h₃yé-, sarciō ‘I mend’ < *sr̥kyé-. Witczak’s article gives Latin fariō ‘salmon trout’, compared with the Germanic sturgeon word family and derived from *sr̥Hyón-; but this also seems to come from Old Latin sariō, thus aligning with the previous group. That these all have -ar- rather than the usual -or- as the reflex of *r̥ however probably indicates a relatively early epenthesis of *ə > *a. Schriver reconstructs a rule *CCCC- > *CaCCC- being already common Italo-Celtic (argued in full in The Reflexes of the Proto-Indo-European Laryngeals in Latin).
At any rate, the moral is that simplifications or epentheses in consonant clusters of the shape *CR might make a more general opening for investigating the history of the PIE syllabic sonorants.
I’ve another example as well, though probably less illustrative. Sticking still to the European languages, there is perhaps something to be made of PIE *Tl-. Word-initially this was a rare cluster, but one established example is *dl̥h₁gʰos ‘long’ (> e.g. Slavic *dьlgъ, Greek δολιχός, Sanskrit dīrgha-). Now, the Baltic languages are known to have word-medially eliminated *-tl-, *-dl- by dissimilation to *-kl-, *-gl-. So would we find a similar initial development here?
We do not; but we do find something unusual: wholesale loss of the initial consonant, resulting in Lith. ilgas, Latv. ilgs! Perhaps this could be again explained by assuming word-initial *Tl-, *Tl̥- > *l-, *l̥-, already before *l̥ > *il? A previously known case with non-syllabic *Tl- is Lith. lokys, Latv. lācis ‘bear’ ~ Old Prussian clokis ‘bear’ (which would then show that this simplification is Eastern Baltic specifically). Unfortunately, there are again also several counterexamples with *Tl̥- > *Til-, e.g. Lith. tiltas, Latv. tilts ‘bridge’ < *tl̥h₂tós. Go figure…
 This post has been prompted by me resuming work for a little while on constructing a reference table on the fate of PIE consonant clusters on Wikipedia.
 Jānis Endzelīns (1973), Comparative Phonology and Morphology of the Baltic Languages: 73 informs that other dialects of Lithuanian, however, do have this change, and so we can also rule out this as a datapoint in favor of a Latvian-Slavic grouping (as has sometimes been suggested). Interestingly even Old Prussian has this epenthesis, so this all could instead testify for the Latvian-Lithuanian split, maybe even some of the inter-Lithuanian dialect splits, going quite a while back. — Most evidence I’ve seen in favor of the East Baltic group in fact looks quite easy to reinterpret as more or less areal: e.g. the sound change bundle *ai > *ei > *ē > ie is basically trivial, and has parallels in most neighboring languages (the first in Slavic, Scandinavian and core Finnic; the second in Swedish and Livonian, as well as Slavic in a different form; the last in Western Slavic and in most of Finnic).
 I’m not going to start probing the issue, but a sound change or two along the lines of *št > *st might also help in explaining the famously inconsistent application of RUKI in Baltic; e.g. Lith. pisti (not ˣpišti) ‘fucks’ ← PIE √peis- ‘to crush, push’.
— It also just now occurs to me that western Uralic *pisə- ‘to put, stick (in)’ (Samic, Finnic, Mordvinic, Mari) is probably derived from this last-mentioned IE root. This contrasts with widespread native Uralic counterparts: #pënə- ‘to put’ (absent only from Samic and Hungarian), #texə- (maybe *tejwä-??) ‘to push’ (F, P, Hu, Ms, Kh), *puskə- ‘to poke’ (S, F, Ms, Kh), which is usually a good indication for an innovation of some sort.
 An old idea, but only recently named and reviewed by Kloekhorst. — I would suggest though that his group of six counterexamples involving derivatives of the type *CeḰ-ro- should not be accounted by “phonetically regular analogy”: they might rather indicate Weise’s Law applying only to syllable-initial palatovelars (*Ḱr-, *-Ḱr̥-) but not to syllable-final ones (*-Ḱ.r-). This would also cover his three counterexamples of the shape *CeḰ-ru-, in which case there is then no need to date the law as any older than common Satemic.
 Schrijver, Peter (2015): “Pruners and trainers of the Celtic family tree“.