Stereoscopic/3D image and video quality assessment (IQA/VQA) has become increasing relevant in today's world, owing to the amount of attention that has recently been focused on 3D/stereoscopic cinema, television, gaming, and mobile video. Understanding the quality of experience of human viewers as they watch 3D videos is a complex and multi-disciplinary problem. Toward this end we offer a holistic assessment of the issues that are encountered, survey the progress that has been made towards addressing these issues, discuss ongoing efforts to resolve them, and point up the future challenges that need to be focused on. Important tools in the study of the quality of 3D visual signals are databases of 3D image and video sets, distorted versions of these signals and the results of large-scale studies of human opinions of their quality. We explain the construction of one such tool, the LIVE 3D IQA database, which is the first publicly available 3D IQA database that incorporates ‘true’ depth information along with stereoscopic pairs and human opinion scores. We describe the creation of the database and analyze the performance of a variety of 2D and 3D quality models using the new database. The database as well as the algorithms evaluated are available for researchers in the field to use in order to enable objective comparisons of future algorithms. Finally, we broadly summarize the field of 3D QA focusing on key unresolved problems including stereoscopic distortions, 3D masking, and algorithm development.