NBC owns the Premier League rights and they split the games across NBCSN (primary channel), Premier League Gold extra (3 games a weekend, this dumb online service that's just a cash grab), MSNBC (1? game week), and another channel I can't remember (1 game week?).

TNT has some of the champions league games, and the rest are on Bleacher Report Live -- some new paid online service.

FS1/FS2 has Bundesliga and some MLS games.

ESPN has Serie A, some MLS games. They also seem to have FA Cup, the Championship, and the Carabao Cup on ESPN+.

This is pretty terrible compared to a few years ago. You could see all PL matches via NBCSN or their extra NBCSN extra channels. Some big games would be on NBC proper. Fox/FS1/FS2 had the champions league. Now things are more splintered and you have to pay extra to see everything. In addition to getting the channels, to watch the Champions League + Premier League you have to buy TWO online only services that are both $9.99/mo or $65 and $80 a year.

For this season, the cheapest way to get NBCSN seems to be to use Sling Blue for $25/mo. FuboTV used to be really good, but it looks like they've basically been raising prices each year. Of course, SlingBlue doesn't come with ESPN/ESPN+ but it certainly covers most the PL games and part of the CL games.