Electrohydrodynamic (EHD) printing is a newly emerging additive manufacturing strategy for the controlled fabrication of three-dimensional (3D) micro/nanoscale architectures. This unique superiority makes it particularly suitable for the biofabrication of artificial tissue analogs with biomimetic structural organizations similar to the scales of native extracellular matrix (ECM) or living cells, which shows great potentials to precisely regulate cellular behaviors and tissue regeneration. Here the state-of-the-art advancements of high-resolution EHD bioprinting were reviewed mainly including melt-based and solution-based processes for the fabrication of micro/nanoscale fibrous scaffolds and living tissues constructs. The related printing materials, innovations on structure design and printing processes, functionalization of the resultant architectures as well as their effects on the mechanical and biological properties of the EHD-printed structures were introduced and analyzed. The recent explorations on the EHD cell printing for high-resolution cell-laden microgel patterning and 3D construct fabrication were highlighted. The major challenges as well as possible solutions to translate EHD bioprinting into a mature and prevalent biofabrication strategy were finally discussed.