I will review some results concerning the linear and critical nonlinear wave equations with regularity $$extract_itex$$\dot H^{\frac{1}{2}}\times \dot H^{-\frac{1}{2}}(\mathbb{R}^d)$$/extract_itex$$. In particular, in the nonlinear case, which includes the cubic wave equation in three dimensions, I will explain how to deal with the lack of compactness due to the Lorentz symmetry.