PBW degenerations and FFLV bases

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.