Mode choice depends on observable characteristics of the transport modes and of the decision maker, but also on unobservable characteristics, known as latent variables. By means of an integrated choice and latent variable (ICLV) model, which is a combination of structural equation model and discrete choice model, it is theoretically possible to integrate both types of variables in a psychologically and economically sound mode choice model. To achieve such a goal requires clear positioning on the four dimensions covered by ICLV models: survey methods, econometrics, psychology and economics. This article presents a comprehensive survey of the ICLV literature applied to mode choice modelling. I review how latent variables are measured and incorporated in the ICLV models, how they contribute to explaining mode choice and how they are used to derive economic outputs. The main results are: 1) the latent variables used to explain mode choice are linked to individual mental states, perceptions of transport modes, or an actual performed behaviour; 2) the richness of structural equation models still needs to be explored to fully embody the psychological theories explaining mode choice; 3) the integration of latent variables helps to improve our understanding of mode choice and to adapt public policies.