Planetary gearboxes significantly differ from fixed-axis gearboxes and exhibit unique behaviors, which invalidate fault diagnosis methods working well for fixed-axis gearboxes. Much work has been done for condition monitoring and fault diagnosis of fixed-axis gearboxes, while studies on planetary gearboxes are not that many. However, we still notice that a number of publications on condition monitoring and fault diagnosis of planetary gearboxes have appeared in academic journals, conference proceedings and technical reports. This paper aims to review and summarize these publications and provide comprehensive references for researchers interested in this topic. The structures of a planetary gearbox as well as a fixed-axis one are briefly introduced and contrasted. The unique behaviors and fault characteristics of planetary gearboxes are identified and analyzed. Investigations on condition monitoring and fault diagnosis of planetary gearboxes are summarized based on the adopted methodologies. Finally, open problems are discussed and potential research topics are pointed out.