This book addresses the applications of extensively used regression models under a Bayesian framework. It emphasizes efficient Bayesian inference through integrated nested Laplace approximations (INLA) and real data analysis using R. The INLA method directly computes very accurate approximations to the posterior marginal distributions and is a promising alternative to Markov chain Monte Carlo (MCMC) algorithms, which come with a range of issues that impede practical use of Bayesian models.