Big Galois image for p-adic families of modular forms

Classical results by Serre, Momose, Ribet and Papier assert that the
images of Galois representations attached to modular forms are "as
large as possible" in most cases. I explain how their results admit an
analogue for p-adic families of modular forms, and how the images of
the associated Galois representations can be described in terms of
congruences between families of different types.