Tissue engineering requires the precise positioning of mammalian cells and biomaterials on substrate surfaces or in preprocessed scaffolds. Although the development of 2D and 3D bioprinting technologies has made substantial progress in recent years, precise, cell-friendly, easy to use, and fast technologies for selecting and positioning mammalian cells with single cell precision are still in need. A new laser-based bioprinting approach is therefore presented, which allows the selection of individual cells from complex cell mixtures based on morphology or fluorescence and their transfer onto a 2D target substrate or a preprocessed 3D scaffold with single cell precision and high cell viability (93-99% cell survival, depending on cell type and substrate). In addition to precise cell positioning, this approach can also be used for the generation of 3D structures by transferring and depositing multiple hydrogel droplets. By further automating and combining this approach with other 3D printing technologies, such as two-photon stereolithography, it has a high potential of becoming a fast and versatile technology for the 2D and 3D bioprinting of mammalian cells with single cell resolution.