Latent variable models are statistical models that relate a set of observed variables to a set of latent variables. Here we demonstrate the versatility of latent variable models as principled statistical tools which facilitate inference from complex data of different sizes and types. This versatility is illustrated through the development of apposite latent variable models required to analyse complex data generated in a range of substantive settings. Examples include the development of models for clustering observations based on categorical sequence data, spectral data or images, analysing data of mixed type and inferring dietary intake. While the developed models have varied purposes, they share a reliance on a latent variable framework.