Principal component analysis, or more generally subspace recovery, is a fundamental problem related to a plethora of signal processing and machine learning tasks. The question being: can we find the basis of a linear subspace that captures most of the information contained in the data? There are in fact many aspects to this question, as it notably asks for relevant data models, as well as efficient computation methods to obtain the corresponding solution. Thus, it drove research in many fields, such as statistics, geometry, and optimization theory. This presentation will detail a personal overview on this problem divided in four axes: models, optimization, performance analysis, applications.