Domain theory began in an attempt to provide mathematical models for high-level programming languages, an area where it has proved to be particularly useful. It is perhaps the most widely-used method for devising semantic models for such languages. This paper is a survey of some generalizations of domain theory that have arisen in efforts to solve related problems. In each case, a description is given of the problem and of the solution generalizing domain theory it inspired. The problems range from the relation of domain theory to other approaches for providing semantic models, particularly in process algebra, to issues surrounding the notion of a computational model, an approach inspired by the recent work of Abbas Edalat.