In this paper, various results on Iocally optimum detection of signals are reviewed concisely, which are easlily apphcable to weak signal detection problems. In addition, locally optmum rank detection schemes for weak signals are reviewed, which are nonparametric counterparts of the locally optimum detecturs. Examples of practical applications, problems in implementation dnd performance characteristecs of the locally optimum detectors are also discussed, Finally, a fuzzy extension of the generalized Neyman Pearson lemma is briefly discussd.