Blue luminescence (BL) and extended red emission (ERE) are observed as diffuse, optical-wavelength emissions in interstellar space, resulting from photoluminescence by ultraviolet(UV)-illuminated interstellar grains. Faintness and the challenge of separating the BL and ERE from the frequently much brighter dust-scattered continuum present major observational hurdles, which have permitted only slow progress in testing the numerous models that have been advanced to explain these two phenomena. Both the ERE, peaking near 680 nm (FWHM ~ 60 - 120 nm) and the BL, asymmetrically peaking at ~ 378 nm (FWHM ~ 45 nm), were first discovered in the Red Rectangle nebula. Subsequently, ERE and BL have been observed in other reflection nebulae, and in the case of the ERE, in carbon-rich planetary nebulae, H II regions, high-latitude cirrus clouds, the galactic diffuse ISM, and in external galaxies. BL exhibits a close spatial and intensity correlation with emission in the aromatic emission feature at 3.3 micron, most likely arising from small, neutral polycyclic aromatic hydrocarbon (PAH) molecules. The spectral characteristics of the BL also agree with those of fluorescence by PAH molecules with 13 to 19 carbon atoms. The BL phenomenon is thus most readily understood as the optical fluorescence of small, UV-excited aromatic molecules. The ERE, by contrast, though co-existent with mid-IR PAH emissions, does not correlate with emissions from either neutral or ionized PAHs. Instead, the spatial ERE morphology appears to be strictly governed by the density of far-UV (E ≥ 10.5 eV) photons, which are required for the ERE excitation. The most restrictive observational constraint for the ERE process is its exceptionally high quantum efficiency. If the ERE results from photo-excitation of a nano-particle carrier by photons with E ≥ 10.5 eV in a single-step process, the quantum efficiency exceeds 100%. Such a process, in which one to three low-energy optical photons may be emitted following a single far-UV excitation, is possible in highly isolated small clusters, e.g. small, dehydrogenated carbon clusters with about 20 to 28 carbon atoms. A possible connection between the ERE carriers and the carriers of DIBs may exist in that both are ubiquitous throughout the diffuse interstellar medium and both have an abundance of low-lying electronic levels with E ≤ 2.3 eV above the ground state.