Despite considerable progress for the regenerative medicine, repair of full-thickness articular cartilage defects and osteochondral interface remains challenging. This low efficiency is largely due to the difficulties in recapitulating the stratified zonal architecture of articular cartilage and engineering complex gradients for bone-soft tissue interface. This has led to increased interest in three-dimensional (3D) printing technologies in the field of musculoskeletal tissue engineering. Printable and biocompatible hydrogels are attractive materials for 3D printing applications because they not only own high tunability and complexity, but also offer favorable biomimetic environments for live cells, such as porous structure, high water content, and bioactive molecule incorporation. However, conventional hydrogels are usually mechanically weak and brittle, which cannot reach the mechanical requirements for repair of articular cartilage defects and osteochondral interface. Therefore, the development of elastic and high-strength hydrogels for 3D printing in the repairment of cartilage defects and osteochondral interface is crucial. In this review, we summarized the recent progress in elastic and high-strength hydrogels for 3D printing and categorized them into six groups, namely ion bonds interactions, nanocomposites integrated in hydrogels, supramolecular guest–host interactions, hydrogen bonds interactions, dynamic covalent bonds interactions, and hydrophobic interactions. These 3D printed elastic and high-strength hydrogels may provide new insights for the treatment of osteochondral and cartilage diseases.