The application of acoustic and optical waves to exert non-contact forces on microscopic and mesoscopic objects has grown considerably in importance in the past few decades. Different physical principles govern the acoustic and optical forces, leading to diverse biomedical applications. Biocompatibility is crucial, and useful optical and acoustic forces can be applied in devices that maintain local heating to acceptable levels. Current acoustic and optical devices work on complementary length scales, with both modalities having useful capabilities at the scale of the cell. Optical devices also cover sub-cellular scales and acoustic devices super-cellular scales. This complementarity has led to the emergence of multi-mode manipulation, often with integrated imaging. In this Technical Review, we provide an overview of optical and acoustic forces, before comparing and contrasting the use of these modalities, or combinations thereof, in terms of sample manipulation and suitability for biomedical studies. We conclude with our perspective on the applications in which we expect to see notable developments in the near future. KEY POINTS • Acoustic and optical forces are governed by different physical principles, but both enable the application of non-contact forces to biomedically important objects such as cells and microorganisms. • Acoustic and optical forces in the pico-Newton to nano-Newton range can be applied to a typical cell, with optical devices having capabilities extending below this scale and acoustic devices above. • Biocompatibility cannot be assumed as both modalities can produce local heating; however, careful device design has led to many examples of biocompatible devices. • Biomedical applications of optical and acoustic devices are rapidly increasing and include manipulation, patterning and mechanical probing, often combined with imaging. • The number of applications is expected to increase, and we anticipate more examples of multimode or hybrid devices to emerge, increasingly sophisticated integration of imaging and the development of more versatile and fully reconfigurable manipulation systems.