This article addresses the fault tolerant control (FTC) issue for a class of hybrid systems (HS) modelled by hybrid automata. Two kinds of faults are considered: continuous fault that affects each continuous system mode; discrete fault that affects the switching conditions. In these two faulty cases, the FTC design has two main objectives: (1) maintain the continuous performances including various stabilities of the origin and the output tracking/regulation behaviours along the trajectories of HS; (2) maintain the discrete specifications that have to be followed by HS, e. g. a desired switching sequence. The following three FTC methodologies are considered: FTC for HS with continuous stability goal; FTC for HS with discrete specifications; supervisory FTC design via hybrid control techniques. Some perspectives are also provided. This article provides the readers a survey on the main techniques that can be used to achieve these FTC goals of HS.