Yamabe flow is an intrinsic geometric flow that deforms the metric of a Riemannian manifold. If the flow converges, it deforms the metric to a metric of constant scalar curvature with the sign depending on the sign of the Yamabe invariant. However convergence of the flow is an intricate problem, already in the setting of smooth compact manifolds. The problem is surprisingly closely related to the positive mass theorem. We discuss the classical results in the area, as well as the recent progress in the setting of stratified spaces. This is joint work with Gilles Carron and Jorgen Olsen Lye.