We report a multidimensional luminescence microscope providing hyperspectral imaging and time-resolved (luminescence lifetime) imaging for the study of luminescent diamond defects. The instrument includes crossed-polariser white light transmission microscopy to reveal any birefringence that would indicate strain in the diamond lattice. We demonstrate the application of this new instrument to detect defects in natural and synthetic diamonds including N3, nitrogen and silicon vacancies. Hyperspectral imaging provides contrast that is not apparent in conventional intensity images and the luminescence lifetime provides further contrast.