The objective of this paper is to present a comprehensive review of the contemporary techniques for fault detection, diagnosis, and prognosis of rolling element bearings (REBs). Data-driven approaches, as opposed to model-based approaches, are gaining in popularity due to the availability of low-cost sensors and big data. This paper first reviews the fundamentals of prognostics and health management (PHM) techniques for REBs. A brief description of the different bearing-failure modes is given, then, the paper presents a comprehensive representation of the different health features (indexes, criteria) used for REB fault diagnostics and prognostics. Thus, the paper provides an overall platform for researchers, system engineers, and experts to select and adopt the best fit for their applications. Second, the paper provides overviews of contemporary REB PHM techniques with a specific focus on modern artificial intelligence (AI) techniques (i.e., shallow learning algorithms). Finally, deep-learning approaches for fault detection, diagnosis, and prognosis for REB are comprehensively reviewed.