The relation between modular forms and Galois representations is more popular than ever, thanks to recent progress on the Fontaine-Mazur conjecture by Kisin, and on Serre's conjecture by Khare and Wintenberger. After a short introduction to this circle of ideas, I will discuss ongoing work on higher-dimensional generalizations, in the context of Gross' philosophy of modular Galois representations. I will attempt to make the talk as self-contained and accessible as possible.