This paper deals with methods and experiences of incorporating a priori knowledge into mathematical models of industrial processes and systems. Grey box modelling has been developed in several directions and can be grouped into branches depending on the way a priori knowledge is handled. In this paper we divide the groups into the following branches; constrained black box identification, semi-physical modelling, mechanistic modelling and hybrid modelling. Experiences from case studies demonstrate the different branches of grey box modelling procedures. In the applications, the grey box models have been used for model based control, soft sensors, process supervision and failure detection