This is an overview of a unified methodology for fitting parametric and nonparametric regression models, including additive models, multilevel models, and models with one or more functional covariates. We also discuss an associated R-package called iprior. An I-prior is an objective prior for the regression function, and is based on its Fisher information. The regression function is estimated by its posterior mean under the I-prior, and scale parameters are estimated via maximum marginal likelihood using an Expectation-Maximization (EM) algorithm. Regression modelling using I-priors has several attractive features: it requires no assumptions other than those pertaining to the model of interest; estimation and inference is relatively straightforward; and small and large sample performance can be better than Tikhonov regularization. We illustrate the use of the iprior package by analysing three well- known data sets, in particular, a multilevel data set, a longitudinal data set, and a dataset involving a functional covariate.