Latent variables that should be measured by multiple observed variable are common in substantive research. Structural equation models (SEMs), which can be regarded as regression models with observed and latent variables, are useful models to assess interrelationships among these variables and have been widely applied to many fields. When applied with data augmentation and recent techniques in statistical computing, the Bayesian approach has been found to be a powerful tool for analysing many important extensions of the basic SEMs. Here, we introduce the basic SEM, present a brief discussion on the Bayesian approach and illustrate it with a simulation study, and review some recent extension, such as two‐level SEMs, transformation SEMs, and nonparametric SEMs. WIREs Comput Stat 2014, 6:276–287. doi: 10.1002/wics.1311This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory