The votes are not in yet, but is seems that the exit polls are giving us a fair idea of what the next European Parliament will look like:
S&D Group (PES): 185
ECR Group: 40
Others (New parties not yet part of a group): 67
The biggest gain for the far right were in France (Front national), Denmark (the Danish People's Party), and Hungary (Jobbik). The fact that the Front national, the Danish People's Party and UKIP topped the polls nationally shows a bug leap forward for Euroskepticism. (Denmark appears to have voted in favour of a European Patent Court in a referendum yesterday, however). This isn't so much a problem for the workings of the European Parliament - after all the vast majority of people voted for pro-European, or at least pro-status quo, parties - but it will put pressure on some groups, particularly the EPP, to take a more Euroskeptic or "Eurorealist" approach.
With the bloc of "others/NI" it will be interesting to see how the groups on the right deal with the new entrants: will the ECR and/or the EFD attract these new entrants. UKIP (EFD) has ruled out working with the Front national, but the Front national has ruled out working with Jobbik or Golden Dawn, so it's still not clear how this new "NI" bloc will work in practice.
On the Presidential race, it looks like the EPP has won and Juncker will have the first opportunity to form a majority in Parliament. The language has changed slightly here, in a predictable way, from a straight presidential race to a more prime ministerial one: the biggest party has the first chance to form a majority, and then the next one, and so on. The difference here is that the candidates probably need an outright win plus a majority to convince the European Council to give way to the European Parliament on the issue of who leads the Commission - something that the EUCO isn't happy to let go of.
Schulz hasn't given up on his hopes of getting the job, though it's become far less likely in practice. The election of a Commission President requires an absolute majority of the Parliament, which is 376. EPP + ECR + ALDE = 323; S&D + ALDE + Greens = 311; and S&D + EPP = 397. While these numbers aren't final, it's clear that a left or right-wing bloc would struggle to command a majority in the Parliament (and that's before you take into account that some MEPs might not vote along the party line since they vote by secret ballot).
There is speculation that there will be a compromise candidate from outside the Europarty candidates - such as Christine Lagarde or Pascal Lamy. The European Parliament should avoid falling into this trap and agree on voting for one of the candidates that ran. Based on these numbers, I don't think it's possible for Schulz to take the post, but perhaps Juncker could be made Commission President and the PES can control some key DGs of the Commission. This would be more in line with the parliamentary nature of the system, but the European Council will strongly resist parliamentary influence over the Commission.
In the coming days and weeks the announcements and spin from the Juncker camp and the various heads of government will reveal the direction of travel here: how much does Juncker really want the job, and if he's bought off with the Presidency of the European Council, would Schulz be able to insert himself into the Commission (unlikely)? Will the Council try to force a compromise candidate on the Parliament? Finally, the politicking of the Europarties will matter a lot: if they don't find a way to hang together as a majority coalition (while maximising their various interests), then the European Parliament will lose its battle to make the Commission more democratically accountable to it, and it will make it extremely difficult to build on the idea that the EP elections can be the equivalent of a government-changing election at the European level.
MEPs should try to remember in the coming months that their own influence and relevance will be dependent on how they fight their next political battle.