Minimal invasive tumor therapies are getting ever more sophisticated with novel treatment approaches and new devices allowing for improved targeting precision. Applying these effectively requires precise localization of the structures of interest. Vital processes, such as respiration and heartbeat, induce organ motion, which cannot be neglected during therapy. This review focuses on 4D organ models to compensate for respiratory motion during therapy. An overview is given on the effects of motion on the therapeutical outcome, methods required to capture and quantify respiratory motion, range of reported tumor motion, types of surrogates used when tumors are not directly observable, and methods for temporal prediction of surrogate motion. Organ motion models, which predict the location of structures of interest from surrogates measured during therapy, are discussed in detail.