High-harmonic generation (HHG) produces ultrashort pulses of extreme ultraviolet radiation (XUV), which can be used for pump-probe transient absorption spectroscopy in metal oxides, semiconductors, and dielectrics. Femtosecond transient absorption on iron and cobalt oxides identifies ligand-to-metal charge transfer as the main spectroscopic transition, rather than metal-to-metal charge transfer or d-d transitions, upon photoexcitation in the visible. In silicon, attosecond transient absorption reveals that electrons tunnel into the conduction band from the valence band under strong-field excitation, to energies as high as 6 eV above the conduction band minimum. Extensions of these experiments to other semiconductors, such as germanium, and other transition metal oxides, such as vanadium dioxide, are discussed. Germanium is of particular interest because it should be possible to follow both electron and hole dynamics in a single measurement using transient XUV absorption.