Fluorescence microscopy allows for the high-throughput imaging of cellular activity across brain areas in mammals. However, capturing rapid cellular dynamics across the curved cortical surface is challenging, owing to trade-offs in image resolution, speed, field of view and depth of field. Here we report a technique for wide-field fluorescence imaging that leverages selective illumination and the integration of focal areas at different depths via a spinning disc with varying thickness to enable video-rate imaging of previously reconstructed centimetre-scale arbitrarily shaped surfaces at micrometre-scale resolution and at a depth of field of millimetres. By implementing the technique in a microscope capable of acquiring images at 1.68 billion pixels per second and resolving 16.8 billion voxels per second, we recorded neural activities and the trajectories of neutrophils in real time on curved cortical surfaces in live mice. The technique can be integrated into many microscopes and macroscopes, in both reflective and fluorescence modes, for the study of multiscale cellular interactions on arbitrarily shaped surfaces.