The focus of research works on cavitation has changed since the 1960s; the behaviour of a single bubble is no more the area of interest for most scientists. Its place was taken by the cavitating flow considered as a whole. Many numerical models of cavitating flows came into being within the space of the last fifty years. They can be divided into two groups: multi-fluid and homogeneous (i.e., single-fluid) models. The group of homogenous models contains two subgroups: models based on transport equation and pressure based models. Several works tried to order particular approaches and presented short reviews of selected studies. However, these classifications are too rough to be treated as sufficiently accurate. The aim of this paper is to present the development paths of numerical investigations of cavitating flows with the use of homogeneous approach in order of publication year and with relatively detailed description. Each of the presented model is accompanied by examples of the application area. This review focuses not only on the list of the most significant existing models to predict sheet and cloud cavitation, but also on presenting their advantages and disadvantages. Moreover, it shows the reasons which inspired present authors to look for new ways of more accurate numerical predictions and dimensions of cavitation. The article includes also the division of source terms of presented models based on the transport equation with the use of standardized symbols.