Strichartz inequalities first appeared in a paper by Strichartz: "Restriction of Fourier Transform to Quadratic Surfaces and Decay of Solutions of Wave Equations. Duke Math. Journal, 44, 1977". They have become a fundamental tool in the study of well posedness of the Cauchy problem for nonlinear evolution equations, such as nonlinear wave or nonlinear Schrödinger equations. In harmonic analysis they are connected to $L^p$ estimates for spectral projectors. In this talk, I will describe the validity of Strichartz Inequalities for waves inside a strictly convex domain. This is a joint work with O. Ivanovici, R. Lascar and F. Planchon.