The time-dependent Schrödinger equation plays an essential role to understand non-relativistic atomic and molecular processes. This is a linear partial differential equation with a very particular structure. A good model for a problem is usually given by a Hamiltonian operator, which suffices to describe the evolution of the system (for given initial conditions) while preserving many qualitative properties (energy, unitarity, etc.). Unfortunately, in general, analytical solutions for the equations are unknown, even for most simple models, and numerical methods are required. Some techniques frequently used are spectral decomposition or spatial discretisation. In general, one has to solve a system of linear ordinary differential equations. Standard numerical methods do not preserve the qualitative properties mentioned and usually have a significant error propagation along the integration. Then, to get accurate and reliable results can be computationally very expensive. Geometric numerical integration has been developed during the last years and it intends to build numerical methods which preserve most qualitative properties of the exact solution. Some of these methods are developed for problems with similar structure to the Schrödinger equation leading in many cases to improved qualitative and quantitative results. In this talk we review two families of methods: Magnus integrators [1] (for non-autonomous problems) and splitting methods [2] (for systems which are separable in solvable parts). [1] S. Blanes, F. Casas, J.A. Oteo and J. Ros, The Magnus and expansion and some of its applications. Physics Reports. In Press. [2] S. Blanes, F. Casas, and A. Murua, Splitting and composition methods in the numerical integration of differential equations, (arXiv:0812.0377v1).