This talk explores spectral rigidity phenomena appearing in billiard dynamics, with a focus on convex planar billiard-like systems, which include Birkhoff, Symplectic, and Outer billiards. I will present some new rigidity results for the associated action spectrum, which are linked to pointwise properties of Mather's beta-function. Notably, we will observe surprising distinctions in the case of Outer billiards. This work is joint with Misha Bialy and Stefano Baranzini.