Abstract: Algebraic (integrable) connections on an algebraic  curve/variety are known to correspond to (Stokes) local systems, but a  similar statement for G-connections is not obvious. In this talk, we  will describe such a correspondence and place it within a general  framework, namely the nonabelian Hodge correspondence. The talk will  begin with a quick review of the classical theory and then proceed to  explore this nonabelian Hodge correspondence. It will end up with the  construction of moduli spaces for various filtered local systems. Based  on some recent joint work with G. Kydonakis, H. Sun and L. Zhao, and  with H. Sun.