Structural equation models provide a general statistical modelling technique for estimating and testing relationships among variables. Such relationships are often not revealed by standard linear models, but are of importance for understanding mechanisms underlying e.g., production-related diseases, such as mastitis. This paper gives a review of Bayesian structural equation models concerning methodology and identifiability, focused on animal breeding and genetics modelling. Applications of this type of methods in animal breeding are also reviewed critically, with discussion on advantages and disadvantages of these approaches.