The idea of finding extrasolar planets (ESPs) through observations of drops in stellar brightness due to transiting objects has been around for decades. It has only been in the last ten years, however, that any serious attempts to find ESPs became practical. The discovery of a transiting planet around the star HD 209458 (Charbonneau et al. cite{charbonneau}) has led to a veritable explosion of research, because the photometric method is the only way to search a large number of stars for ESPs simultaneously with current technology. To this point, however, there has been limited research into the various techniques used to extract the subtle transit signals from noise, mainly brief summaries in various papers focused on publishing transit-like signatures in observations. The scheduled launches over the next few years of satellites whose primary or secondary science missions will be ESP discovery motivates a review and a comparative study of the various algorithms used to perform the transit identification, to determine rigorously and fairly which one is the most sensitive under which circumstances, to maximize the results of past, current, and future observational campaigns.