Mazur's Program B after Furio--Lombardo

Mazur's Program B is the problem of classifying the possibilities for the images of the Galois representations attached to a non-CM elliptic curve over a number field. The case of ell-adic representations attached to elliptic curves over the rationals has ''almost'' been solved. I'll discuss the most recent progress on this due to Furio--Lombardo and my own ongoing attempt to extend their ideas to other cases (joint with Santiago Arango-Piñeros).