Abstract: In the talk, I will discuss continuously self-similar gravitational dynamics in 1+1 spacetime dimensions. I will show how the assumption of self-similarity fixes the form of the two-dimensional theory, two classes of which are well-known in the literature. I will discuss some exotic static solutions and how inclusion of matter fields leads to non-trivial dynamics. I will argue for the occurrence of singularities based on a simple feature of differential equations. Time permitting, I will also discuss numerical work relating to dynamics of matter field collapse.