Piezoelectric Micromachined Ultrasonic Transducers (PMUT) and Capacitive Micromachined Ultrasonic Transducers (CMUT) have seen great developments in recent years, both in terms of performance and scope of applications within the biomedical ultrasound domain. This paper presents a review of the state-of-the-art of PMUT and CMUT technologies, focusing on their principle of operation, microfabrication techniques and use in different biomedical imaging and therapeutic applications. The advantages and drawbacks of PMUT and CMUT technologies in comparison with conventional bulk transducers are highlighted, the trade-offs among PMUTs and CMUTs are discussed, and their relevance in the current landscape of medical diagnostics and therapeutic uses is outlined, thus providing a clear overview of these promising technologies for the present and the next generation biomedical ultrasound applications.