Symbolic dynamics is a tool that simplifies the study of dynamical systems in various aspects. It is known for almost fifty years that uniformly hyperbolic systems have ``good'' codings. For non-uniformly hyperbolic systems, Sarig constructed in 2013 ``good'' codings for surface diffeomorphisms. In this talk we will discuss some recent developments on Sarig's theory, when the map has discountinuities and/or critical points, such as multimodal maps of the interval and Bunimovich billiards.