Abstract : We will describe thermalization in local and subsystem observables in theories near criticality. We will use the quench set-up to drive the system out of equilibrium. Specifically, in 2D critical theories we shall look at the interplay of thermalization with conformal symmetry. We will point out various universal signatures in various observables. After discussing sudden quenches, we shall look at critical smooth quenches which are also associated with universal scalings. These however are most well understood in free theories. We will go beyond free theories, and discuss smooth quenches in the context of a large N interacting quantum field theory of fermions. In this example, we will discover a universal scaling associated with restoration of a broken symmetry. Finally we will take a look at driven critical systems, which can have islands of non-thermality. We end with some general comments on the approach towards thermalization in critical theories.