Abstract: I will deal with existence and uniqueness results for linear hyperbolic partial differential equations of second order on Lorentzian manifolds. The principal part of a linear strictly hyperbolic operator of second order may be written as the Laplace-Beltrami operator of some Lorentzian metric, thus it is natural to use methods of Lorentzian geometry in the existence theory for this class of PDEs. This geometric viewpoint allows an elegant formulation of the energy estimates in the framework of Sobolev spaces by the use of energy tensors. Recent interest in these techniques arises from generalizations to the case of coefficients of low regularity motivated by applications in general relativity and mathematical geophysics.