In recent years, the field of numerical relativity has obtained several important results, among which the simulation of the coalescence and merger of two black holes. These achievements rely not only on complex numerical algorithms, but primarily on the analytic study of the Einstein equations to obtain stable and numerically well-suited formulations (and gauge choices) for this set of partial differential equations. In this seminar I shall introduce some of these formulations, based on the 3+1 approach, before turning to the description of the high-precision numerical methods, so-called spectral methods, particularly adapted for the description of fields in spherical coordinates. Finally, a brief review about the numerical representation of black holes (puncture of excision methods) shall be sketched.