The quality of experience (QoE) of 3D contents is usually considered to be the combination of the perceived visual quality, the perceived depth quality, and lastly the visual fatigue and comfort. When either fatigue or discomfort are induced, studies tend to show that observers prefer to experience a 2D version of the contents. For this reason, providing a comfortable experience is a prerequisite for observers to actually consider the depth effect as a visualization improvement. In this paper, we propose a comprehensive review on visual fatigue and discomfort induced by the visualization of 3D stereoscopic contents, in the light of physiological and psychological processes enabling depth perception. First, we review the multitude of manifestations of visual fatigue and discomfort (near triad disorders, symptoms for discomfort), as well as means for detection and evaluation. We then discuss how, in 3D displays, ocular and cognitive conflicts with real world experience may cause fatigue and discomfort; these includes the accommodation-vergence conflict, the inadequacy between presented stimuli and observers depth of focus, and the cognitive integration of conflicting depth cues. We also discuss some limits for stereopsis that constrain our ability to perceive depth, and in particular the perception of planar and in-depth motion, the limited fusion range, and various stereopsis disorders. Finally, this paper discusses how the different aspects of fatigue and discomfort apply to 3D technologies and contents. We notably highlight the need for respecting a comfort zone and avoiding camera and rendering artifacts. We also discuss the influence of visual attention, exposure duration, and training. Conclusions provide guidance for best practices and future research.