The I-prior methodology is a new modelling technique which aims to improve on maximum likelihood estimation of linear models when the dimensionality is large relative to the sample size. By putting a prior which is informed by the dataset (as opposed to a subjective prior), advantages such as model parsimony, lesser model assumptions, simpler estimation, and simpler hypothesis testing can be had. By way of introducing the I-prior methodology, we will give examples of linear models estimated using I-priors. This includes multiple regression models, smoothing models, random effects models, and longitudinal models. Research into this area involve extending the I-prior methodology to generalised linear models (e.g. logistic regression), Structural Equation Models (SEM), and models with structured error covariances.