Bayesian model class selection has attracted substantial interest in recent years for selecting the most plausible/suitable class of models based on system input-output data. The Bayesian approach provides a quantitative expression of a principle of model parsimony or of Ockham's razor which in engineering applications can be stated as simpler models are to be preferred over unnecessarily complicated ones. In this paper, some recent developments are reviewed. Linear and nonlinear regression problems are considered in detail. Bayesian model class selection is particularly useful for regression problems since the regression formula order is difficult to be determined solely by physics due to its empirical nature. Applications are presented in different areas of civil engineering, including artificial neural network for damage detection and seismic attenuation empirical relationship.