The <a href="http://www.science.unitn.it/~bagagiol/NotesByCardaliaguet.pdf">lecture notes</a> on mean-field games of <A HREF="https://en.wikipedia.org/wiki/Pierre-Louis_Lions">Lions</A>, from a course at the Collège de France, have been typed out by Pierre Cardaliaguet. They address both optimal control and dynamic programming. I would think it will be hard to beat these for an authoritative exposition. For a summary of open problems you could look <A HREF="https://link.springer.com/article/10.1007/s11537-007-0657-8">here.</A>