Hyaline cartilage is deficient in self-healing properties. The early treatment of focal cartilage lesions is a public health challenge to prevent long-term degradation and the occurrence of osteoarthritis. Cartilage tissue engineering represents a promising alternative to the current insufficient surgical solutions. 3D printing is a thriving technology and offers new possibilities for personalized regenerative medicine. Extrusion-based processes permit the deposition of cell-seeded bioinks, in a layer-by-layer manner, allowing mimicry of the native zonal organization of hyaline cartilage. Mesenchymal stem cells (MSCs) are a promising cell source for cartilage tissue engineering. Originally isolated from bone marrow, they can now be derived from many different cell sources (e.g., synovium, dental pulp, Wharton’s jelly). Their proliferation and differentiation potential are well characterized, and they possess good chondrogenic potential, making them appropriate candidates for cartilage reconstruction. This review summarizes the different sources, origins, and densities of MSCs used in extrusion-based bioprinting (EBB) processes, as alternatives to chondrocytes. The different bioink constituents and their advantages for producing substitutes mimicking healthy hyaline cartilage is also discussed.