Quality is one of the most debated topics in the recent history of mixed methods research. A growing number of authors are currently discussing how the quality of mixed methods research should be conceptualised and operationalised, with the ultimate aim of promoting well designed and properly implemented mixed methods studies. These authors argue that mixed methods research has a number of unique features with respect to monomethod research and, as such, should be appraised according to its own set of quality criteria. Based on a systematic search of the literature, this review (1) examines the features and trends of the literature on the quality of mixed methods research published until February 2016; (2) provides a metasummary of the most prevalent quality criteria suggested in this literature; and (3) proposes a number of recommendations for future discussion and research on this topic. The review concludes that (1) publications on the quality of mixed methods research are increasingly more prevalent and elaborated; (2) a shared set of core quality criteria for appraising mixed methods research can be identified across publications; and (3) future work on this topic should focus on increasing the number of empirical publications on quality, achieving greater consistency in quality terminology, and reaching an agreement on core quality criteria.