I will give an overview of the relatively young theory of PBW degenerations of highest weight modules and flag varieties. In particular, I will talk about the so-called Feigin-Fourier-Littelmann-Vinberg bases in irreducible representations in types A and C. I will also try to present some more recent developments concerning these bases and the corresponding lattice polytopes.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/158