We present a table-top extreme ultraviolet (XUV) beamline for measuring time- and frequency-resolved XUV-excited optical luminescence (XEOL) with additional femtosecond-resolution XUV transient absorption spectroscopy functionality. XUV pulses are generated via high-harmonic generation using a near-infrared pulse in a noble gas medium and focused to excite luminescence from a solid sample. The luminescence is collimated and guided into a streak camera where its spectral components are temporally resolved with picosecond temporal resolution. We time-resolve XUV-excited luminescence and compare the results to luminescence decays excited at longer wavelengths for three different materials: (i) sodium salicylate, an often used XUV scintillator; (ii) fluorescent labeling molecule 4-carbazole benzoic (CB) acid; and (iii) a zirconium metal oxo-cluster labeled with CB, which is a photoresist candidate for extreme-ultraviolet lithography. Our results establish time-resolved XEOL as a new technique to measure transient XUV-driven phenomena in solid-state samples and identify decay mechanisms of molecules following XUV and soft-x-ray excitation.