Venereal disease is among one of the more active serious epidemics in the world today. Despite its prevalence and the ever-increasing literature on the mathematical treatment of epidemics very little progress has been made toward modelling the spread of this disease. Key features of the disease that help to account for this lack of progress are: (i) VD involves the cross-infection between two groups of individuals and (ii) VD is a recurrent disease. The heterosexual spread .of VD ties in the modelling of this disease with the yet unsolved problem in mathematical biology concerning the growth of two interacting species. In this paper we review the current state of the art in the stochastic modelling of this disease.