We present angle- and polarization-resolved cathodoluminescence (CL) imaging spectroscopy as a technique to probe the optical properties of photonic nanostructures. The 30 keV electron beam is raster-scanned over the sample and an optical excitation map, reflecting the local optical density of states, is made at a resolution determined by the electron spot size (< 10 nm), well below the optical diffraction limit. From the images the dispersion and local modes of resonant plasmonic and dielectric nanostructure are directly determined. In angle-resolved mode, the azimuthal and zenithal CL emission distributions are measured, probing the angular radiation profile of optical nanoantennas and allowing for momentum spectroscopy to reconstruct the optical band structure of photonic crystals. In polarization-resolved mode, the full polarization state of the emitted light is determined, allowing distinction between linearly and circularly polarized light in a spatially and angle-resolved way. In tomographic mode, 2D CL images are taken under multiple angles of incidence, and a 3D image of the local field distributions is obtained from a tomographic construction. The CL microscope is based on a specially designed piezo-electrically controlled parabolic mirror assembly, and a dedicated optical detection and imaging system operating over the entire UV-VIS-NIR spectral range.