There has been much research over the past two decades with the aim of engineering cartilage constructs for repairing or restoring damaged cartilage. To engineer healthy neocartilage, the constructs must have mechanical properties matching those of native cartilage as well as appropriate for the loading conditions of the joint. This article discusses the mechanical behavior of native cartilage and surveys different types of tensile, compressive, and shear tests with their limitations. It also comprehensively reviews recent work and achievements in developing the mathematical models representing the mechanical properties of both native and engineered cartilage. Different methods for enhancing the mechanical properties of engineered cartilage are also discussed, including scaffold design, mechanical stimulation, and chemical stimulation. This article concludes with recommendations for future research aimed at achieving engineered cartilage with mechanical properties matching those found in native cartilage.