ESR-dating is based on the measurement of unpaired electrons trapped in crystal defects. These quasi free electrons are produced over geologic time by the natural radiation originated from the decay of radioactive elements and cosmic radiation. This work displays comprehensively the physical basis of ESR-spectroscopy and some major problems of the determination of the accumulated dose and of the annual dose, respectively. ESR-dating is applied to various materials: bones and teeth, biogene carbonates, travertines, speleothems, and some additional minerals. Here specific dating problems are discussed: uranium-accumulation in bones and teeth, evaluation of spectra, and stability of traps. Systematic ESR-dating of speleothems give evidence for some paleoclimatic interpretations. -- AATA