Microscale surgery on single cells and small organisms has enabled major advances in fundamental biology and in engineering biological systems. Examples of applications range from wound healing and regeneration studies to the generation of hybridoma to produce monoclonal antibodies. Even today, these surgical operations are often performed manually, but they are labor intensive and lack reproducibility. Microfluidics has emerged as a powerful technology to control and manipulate cells and multicellular systems at the micro- and nanoscale with high precision. Here, we review the physical and chemical mechanisms of microscale surgery and the corresponding design principles, applications, and implementations in microfluidic systems. We consider four types of surgical operations: (1) sectioning, which splits a biological entity into multiple parts, (2) ablation, which destroys part of an entity, (3) biopsy, which extracts materials from within a living cell, and (4) fusion, which joins multiple entities into one. For each type of surgery, we summarize the motivating applications and the microfluidic devices developed. Throughout this review, we highlight existing challenges and opportunities. We hope that this review will inspire scientists and engineers to continue to explore and improve microfluidic surgical methods.