The separation of isotopes by photochemical processes employing high power lasers has received much attention during the past years. The method promises very efficient and economically competitive separation processes for a large number of isotopes, most notably uranium. Although no laser separation experiment has as yet produced weighable quantities of isotopic materials to date, a number of very recent experiments have shown the viability of the fundamental concepts. We shall review the basic concepts and the existing experimental work. In the course of this review we shall try to point out a number of unresolved problems open to research and discuss the requirements for the further development of high-power lasers for isotope separation. Finally, we will discuss possible applications of isotopes other than uranium and investigate the uses and the economics of titanium-50 as a large scale construction material for nuclear reactors.