Passive acoustic aircraft and wake localization methods rely on the noise emission from aircraft and their wakes for detection, tracking, and characterization. This paper takes a holistic approach to passive acoustic methods and first presents a systematic bibliographic review of aeroacoustic noise of aircraft and drones, followed by a summary of sound generation of wing tip vortices. The propagation of the sound through the atmosphere is then summarized. Passive acoustic localization techniques utilize an array of microphones along with the known character of the aeroacoustic noise source to determine the characteristics of the aircraft or its wake. This paper summarizes the current state of knowledge of acoustic localization with an emphasis on beamforming and machine learning techniques. This review brings together the fields of aeroacoustics and acoustic-based detection the advance the passive acoustic localization techniques in aerospace.