In the last ten years stereology has drastically changed its state, and it seems that this process will continue in the future. This applies to its practical methods as well as to its theoretical fundamentals. Thus it may be justified to publish now a further review paper on stereology in this journal, following the papers by Ripley (1984) and Jensen et al. (1985) or other excellent review papers such as Miles (1987a) and Cruz-Orive (1987b, c). The present author hopes that his particular standpoint will make the current discussion on stereology and its future more colourful. An important topic of this paper is the relations between stereology and stochastic geometry (Stoyan, Kendall & Mecke, 1987), which gives the theoretical foundation of modern stereology. Furthermore, some open problems of stereology are posed. Finally, some of the new developments of stereology, such as second-order methods or disector and selector, are discussed from the standpoint of the so-called model approach.