I will present recent developments in the theory of overconvergent F-isocrystals, the p-adic analogue of l-adic lisse sheaves. For the most part of the talk I will focus on the parabolicity conjecture, a conjecture proposed by Crew in '92 on the algebraic monodromy groups of F-isocrystals. In the end, I will explain how monodromy groups of F-isocrystals can be used to study the variation of algebraic cycles in positive characteristic.