Some aspects of p-adic Siegel modular forms

In joint work with S.Nagaoka we try to generalize Serre's theory of p-adic modular forms to Siegel modular forms, using congruences for Fourier coefficients (not Hecke eigenvalues!). Some results generalize in a straightforward way (with proofs different from the classical ones), other results need subtle modification, in particular
for vector-valued modular forms. We will give a survey of our work on this topic.