Here are some possible crimes that have been committed.
Campaign finance laws – Basically soliciting a thing of value from a foreign national to affect an election. (52 USC 30121 and/or 36 USC 510)
Klein Conspiracy – A Klein conspiracy exists when one conspiracies to “impair or impede” the lawful functions of the federal government. In this case the lawful function of government would be the administration of fair elections which were impaired by actions taken by Russia in collusion with the Trump Campaign. (18 USC Section 371)
Obstruction of Justice - This rule basically says that whoever corruptly or by threats of force, or by any threatening letter or communication, influences, obstructs, or impedes, or endeavors to influence, obstruct or impede, the due administration of justice shall be guilty of an offense. (18 USC 1503)
There is no crime for "collusion" as such. This is a term of convenience or perhaps one that was used early on and just stuck. I think in general when people say collusion it really means one of the above first two listed crimes have been committed. It's like saying "cahoots". But if you can establish that the Trump Campaign was in cahoots with the Russians or colluded with the Russians in the interference or meddling of our election by the Russians, then you can probably find a criminal code that applies. We do have laws that protect our democratic process.
In the case of Trump's campaign, the two most probable events that were criminal - that we know of - were (with the exception of Obstruction of Justice, which also is a crime) the Genius Junior meeting with the Russians (the "I Love It!" meeting) and the Papadopulos activities.
If proven, the Genius Junior meeting will probably fall into the category of campaign finance laws, since the dirt was a thing of value and that dirt was used to influence the election (the release of Hillary's emails). Since we don't know all the facts, it could perhaps be a Klein Conspiracy. We don't know.
The Papadopulos deal could also be a "thing of value" election crime, or perhaps it is a conspiracy to violate the Computer Fraud and Abuse Act.
It appears to me that Roger Stone and Peter Smith might have conducted a Klein Conspiracy as they seemed to want to help the Russians distribute the stolen emails. How much Trump knew about this is unknown.
Of course Mueller is also looking at Obstruction of Justice. Many think he need look no further than the James Comey firing. If he brings this charge, however, I suspect it will be a lot more complex than just the James Comey firing, as Trump has done a number of things that will collectively help build a case for Obstruction of Justice.