Gravitational waves from inspiraling sub-solar mass compact objects would provide almost definitive evidence for the existence of primordial black holes. In this chapter, we explain why these exotic objects are interesting candidates for current and future gravitational-wave observatories, and provide detailed explanations of how they are searched for. We describe one method, matched filtering, to search for binaries with masses in \([0.01,1]M_\odot \) . Furthermore, since signals from inspiraling planetary- and asteroid-mass compact binaries ( \([10^{-9},10^{-2}]M_\odot \) ) would spend hours to years in the detector frequency band, we explain the novel pattern recognition techniques that have been developed to search for them. Finally, we describe extreme mass ratio inspiral systems, and how these will be searched for in future space-based detectors. For all mass regimes, we comment on the prospects for detection.