Online monitoring of Partial Discharges (PDs) in rotating electrical machines is an useful tool for machine prognosis, as it presents reduced costs compared to intrusive inspections and is associated with relevant problems. Although this monitoring method has been developed for almost 50 years, the recent advancements in processes automation and signal processing techniques allow improvements that are still being studied by academic and industrial researchers. To analyze the current context of PDs monitoring, this article presents a literature review based on concepts of PDs in rotating machines, data acquisition techniques, state-of-the art commercial equipment, and recent methodologies for detection and pattern recognition of PDs. The challenges identified in the literature that motivate the development of more reliable and robust PD monitoring systems are presented and discussed.