The introduction of living cells to manufacturing process has enabled the engineering of complex biological tissues in vitro. The recent advances in biofabrication with extremely high resolution (e.g. at single cell level) have greatly enhanced this capacity and opened new avenues for tissue engineering. In this review, we comprehensively overview the current biofabrication strategies with single-cell resolution and categorize them based on the dimension of the single-cell building blocks, i.e. zero-dimensional single-cell droplets, one-dimensional single-cell filaments and two-dimensional single-cell sheets. We provide an informative introduction to the most recent advances in these approaches (e.g. cell trapping, bioprinting, electrospinning, microfluidics and cell sheets) and further illustrated how they can be used in in vitro tissue modelling and regenerative medicine. We highlight the significance of single-cell-level biofabrication and discuss the challenges and opportunities in the field.