The subject of absorption by bound electrons of dark matter in the form of dark photons and axion-like particles, as well as of dark photons from the Sun, in current and next-generation direct detection experiments will be presented. Experiments sensitive to electron recoils can detect such particles with masses between a few eV to more than 10 keV. For dark photon dark matter, an updated bound based on XENON10 data will be presented, as well as new bounds based on data from XENON100 and CDMSlite. These experiments disfavor previously allowed parameter space. Sensitivity projections for SuperCDMS at SNOLAB for silicon and germanium targets, as well as for various possible experiments with scintillating targets (cesium iodide, sodium iodide, and gallium arsenide) will also be presented. The projected sensitivity can probe large new regions of parameter space. For axion-like particles, the same current direction detection data improves on previously known direct-detection constraints but does not bound new parameter space beyond known stellar cooling bounds. However, projected sensitivities of the upcoming SuperCDMS SNOLAB using germanium can go beyond these and even probe parameter space consistent with possible hints from the white dwarf luminosity function. Similar results for dark photons from the sun will be presented as well. For all cases, direct-detection experiments can have unprecedented sensitivity to dark-sector particles.