This paper presents a survey of the numerical simulation of base isolation systems for the vibration control of buildings and their equipment, primarilly against earthquakes. Base isolation has received much attention in the recent twenty years and many buildings have been protected using this technology. The article focusses mainly on the different numerical methods used in the analysis of base isolated buildings. The conventional form of solving the equations of motion governing the seismic response of building structures with nonlinear base isolation consists of using monolithic step by step integration methods. As an effcient alternative, static condensation and block iterative schemes can be applied. The particularities of the equations of motion of buildings equiped with various base isolation systems are described. The linear theory of base isolated buildings is then presented. After this, numerical solution techniques for the analysis of the seismic response of buildings with isolation systems are developed in detail in the paper. Finally, numerical results for elastic and inelastic structures are described. A complete set of references coverning a wide range of studies is included.