Image-guided radiotherapy (IGRT) has helped to dramatically reduce safety margins compensating for positioning uncertainties in radiotherapy. A remaining issue posing problems for photon radiotherapy (RT), but even more so for particle RT, is target motion during treatment delivery. This review outlines the various strategies currently being developed or already in clinical use to compensate for organ motion, predominantly breathing-induced motion of liver and lung targets. Several motion compensation strategies have recently been introduced clinically. Among these are optimized margins encompassing the individual range of target motion, treatment under breath hold, gated treatments, and tumor tracking with a dedicated treatment device. A variety of surveillance strategies for gating and tracking, such as indirect tracking with external fiducial markers and surface scanning devices, direct tracking with implanted electromagnetic markers, fiducial markers, and fluoroscopy, and ultrasound-based tracking are already in clinical use or are under development. Tracked treatment with linear accelerators based on tumor-synchronous MLC- or treatment-table adaptation are moving toward clinical use. A multitude of strategies to reduce the impact of intrafractional target motion in RT have been developed and are increasingly being used clinically. The clinical introduction of advanced strategies currently under development is imminent. After IGRT minimized treatment margins for static tumors, the implementation of motion compensation strategies will achieve the same for targets being subject to intrafractional breathing-induced motion.