This Paper presents an exhaustive review on BIST technique used in different fault tolerant systems and also consider the fault detection methodologies used in these systems. BIST is an alternative method of at-speed testing of high speed ATE that is expensive and having some unavailability issues. With supplement of an external high speed clock, BIST requires on-chip circuitry for vector generation and response analysis. The pseudo-random vectors gives a good coverage of stuck-at faults and transition faults even if it is applied at high speed. But in case of robust testing, the Coverage of path-delay faults requires some additional modifications in the combinational logic. BIST also provide the testing feature to test circuits for timing delay. For this a standard BIST architecture with a hybrid pattern generator is required, for replacing LFSR-TPG, which can test both stuck at and delay faults. For test insertion BIST is now universally adopted, this is not only because BIST hardware overheads have come down, particularly for memory BIST (1-3%) [1], [7], [16] but also because it enables partitioning of the testing problem for large hardware systems into small ones so currently memory BIST is preferred [3], [4], [11], [68], [92], [121], and [122]. Most commonly used schemes to provide pattern generation and response compaction for BIST are LFSRs, MISRs and built-in logic block observers.