The paper first reviews data on HIV infections and AIDS disease among homosexual men, heterosexuals, intravenous (IV) drug abusers and children born to infected mothers, in both developed and developing countries. We survey such information as is currently available about the distribution of incubation times that elapse between HIV infection and the appearance of AIDS, about the fraction of those infected with HIV who eventually go on to develop AIDS, about time-dependent patterns of infectiousness and about distributions of rates of acquiring new sexual or needle-sharing partners. With this information, models for the transmission dynamics of HIV are developed, beginning with deliberately oversimplified models and progressing - on the basis of the understanding thus gained - to more complex ones. Where possible, estimates of the model's parameters are derived from the epidemiological data, and predictions are compared with observed trends. We also combine these epidemiological models with demographic considerations to assess the effects that heterosexually-transmitted HIV/AIDS may eventually have on rates of population growth, on age profiles and on associated economic and social indicators, in African and other countries. The degree to which sexual or other habits must change to bring the `basic reproductive rate', R<latex>$_0$</latex>, of HIV infections below unity is discussed. We conclude by outlining some research needs, both in the refinement and development of models and in the collection of epidemiological data.