The clinical assessment of microvascular pathologies (in diabetes and in inflammatory skin diseases, for example) requires the visualization of superficial vascular anatomy. Photoacoustic tomography (PAT) scanners based on an all-optical Fabry-Perot ultrasound sensor can provide highly detailed 3D microvascular images, but minutes-long acquisition times have precluded their clinical use. Here we show that scan times can be reduced to a few seconds and even hundreds of milliseconds by parallelizing the optical architecture of the sensor readout, by using excitation lasers with high pulse-repetition frequencies and by exploiting compressed sensing. A PAT scanner with such fast acquisition minimizes motion-related artefacts and allows for the volumetric visualization of individual arterioles, venules, venous valves and millimetre-scale arteries and veins to depths approaching 15 mm, as well as for dynamic 3D images of time-varying tissue perfusion and other haemodynamic events. In exploratory case studies, we used the scanner to visualize and quantify microvascular changes associated with peripheral vascular disease, skin inflammation and rheumatoid arthritis. Fast all-optical PAT may prove useful in cardiovascular medicine, oncology, dermatology and rheumatology.