The menisci are a pair of semilunar fibrocartilage structures that play an essential role in maintaining normal knee function. Injury to the menisci can disrupt joint stability and lead to debilitating results. Because natural meniscal healing is limited, an efficient method of repair is necessary. Tissue engineering (TE) combines the principles of life sciences and engineering to restore the unique architecture of the native meniscus. Mesenchymal stem cells (MSCs) have been investigated for their therapeutic potential both in vitro and in vivo. This comprehensive review examines the English literature identified through a database search using Medline, Embase, Engineering Village, and SPORTDiscus. The search results were classified based on MSC type, animal model, and method of MSC delivery/culture. A variety of MSC types, including bone marrow-derived, synovium-derived, adipose-derived, and meniscus-derived MSCs, has been examined. Research results were categorized into and discussed by the different animal models used; namely murine, leporine, porcine, caprine, bovine, ovine, canine, equine, and human models of meniscus defect/repair. Within each animal model, studies were categorized further according to MSC delivery/culture techniques. These techniques included direct application, fibrin glue/gel/clot, intra-articular injection, scaffold, tissue-engineered construct, meniscus tissue, pellets/aggregates, and hydrogel. The purpose of this review is to inform the reader about the current state and advances in meniscus TE using MSCs. Future directions of MSC-based meniscus TE are also suggested to help guide prospective research.