We will present recent developments in the theory of overconvergent F-isocrystals, the p-adic analogue of ell-adic lisse sheaves. For the most part of the talk we will focus on the parabolicity conjecture, a conjecture proposed by Crew in '92 on the algebraic monodromy groups of overconvergent F-isocrystals. Besides the proof, we will explore the main consequences of this conjecture.
