Fast correlation attacks, pioneered by Meier and Staffelbach in 1988, constitute an important class of attacks on stream ciphers. They exploit a correlation between the keystream and the output of a linear feedback shift register (LFSR) within the cipher. Several factors affect the feasibility of such an attack, e.g., the amount of available keystream and the number of taps in the LFSR. Notably, for a fixed number of taps, the length of the LFSR does not affect the complexity of the attack. When the register does not have a sufficiently small number of taps, however, the attacker will try to find parity check equations of low weight, at which point the length of the register does matter. In this paper, we go through the significant contributions to this field of cryptanalysis, reiterating the various algorithms that have been developed for finding parity check equations and performing the online stage on received keystream. We also suggest some new generalizations of Meier-Staffelbach's original formulations.