The topological entropy of geodesic flows has been extensively studied since the foundational works of Dinaburg and Manning. It measures the exponential complexity of the geodesic flow of a Riemannian manifold, and there are several results connecting it to the geometry and topology of a Riemannian manifold. In this talk I will explain how recent results obtained jointly with Dahinden, Meiwes, and Pirnapasov can be used to give a meaningful extension of the topological entropy to C0-Riemannian metrics; i.e. Riemannian metrics which are continuous but not necessarily differentiable. Similarly, using contact geometry I will explain how we can talk in a meaningful way about the topological entropy of convex and starshaped polytopes in R4, thinking of them as C0-contact forms. This is joint work with Matthias Meiwes.