Robotics has a significant potential to enhance the overall capacity and efficiency of healthcare systems. Robots can help surgeons perform better quality operations, leading to reductions in the hospitalisation time of patients and in the impact of surgery on their postoperative quality of life. In particular, robotics can have a significant impact on microsurgery, which presents stringent requirements for superhuman precision and control of the surgical tools. Microsurgery is, in fact, expected to gain importance in a growing range of surgical specialties as novel technologies progressively enable the detection, diagnosis and treatment of diseases at earlier stages. Within such scenarios, robotic microsurgery emerges as one of the key components of future surgical interventions, and will be a vital technology for addressing major surgical challenges. Nonetheless, several issues have yet to be overcome in terms of mechatronics, perception and surgeon-robot interfaces before microsurgical robots can achieve their full potential in operating rooms. Research in this direction is progressing quickly and microsurgery robot prototypes are gradually demonstrating significant clinical benefits in challenging applications such as reconstructive plastic surgery, ophthalmology, otology and laryngology. These are reassuring results offering confidence in a brighter future for high-precision surgical interventions.