•Bio-inks for tissue-specific physicochemical microenvironments.•Combination of zone-specific bioinks and programmed printing paths.•Multichannel extrusion bioprinting technique for reconstructing tissues with anisotropic structure.•External stimulation during bioprinting for regulating cell behaviors. Human tissue consists of various tissue-specific cells, extracellular matrix components and microstructures, and growth factors. With promising multi-cell and multi-material integration manufacturing feature, 3D extrusion bioprinting has shown outstanding application potential in the field of regenerative medicine. For functional tissue regeneration, bioprinted constructs not only play the role of a cell-delivery system, but also serve as an important host niche for cell proliferation and work. In order to meet the specific requirements of different tissue regeneration, development of bio-inks that provide tissue-specific biophysical cues and biochemical microenvironments is an important research topic. Furthermore, reconstruction of tissues with anisotropic structure, such as articular cartilage and meniscus, largely depend on the design of 3D bioprinting path for accurate arrangement of specific bio-inks. This review summarizes the advanced designs of tissue-specific 3D bioprinting of cell-laden constructs for functional regeneration of skeletal and locomotor systems such as bone, cartilage, skeletal muscle, and blood vessels via the collaboration of bio-ink and printing processes. It may provide a basis for synergistic design for functional regenerative constructs bioprinting in the future.