We will introduce and present various results on the characteristic initial value problem for the Einstein equations. We will start with the simpler wave equation on general Lorentzian manifolds and see that the only potential obstructions are conservation laws. We will also see that such conserved charges play an important role in the dynamics of scalar perturbations of black holes. We will then proceed with the non-linear theory for the Einstein equations. We will consider gluing problems close to the Minkowski spacetime. We will finally present a few applications to the Riemannian gluing problem.