This article describes a new microscope, based on angle-resolved cathodoluminescence (CL) imaging spectroscopy, which enables optical imaging and spectroscopy at deep-subwavelength spatial resolution. We used a free electron beam in a scanning electron microscope as a direct excitation source for polarizable materials, and we collected the emitted coherent visible/infrared CL radiation using a specially designed optical collection system that is integrated in the electron microscope. We have demonstrated the use of this new technique for the excitation of plasmons in single metal nanoparticles, surface plasmon polaritons at metal surfaces, resonant Mie modes in dielectric nanostructures, and cavity modes and Bloch modes in photonic crystals. Using angle-resolved detection, we are able to derive the nature of localized modes and the dispersion of propagation modes in dielectric and plasmonic geometries. An outlook about new directions and applications of CL imaging spectroscopy is also provided.