Several recent advances in smoothing and semiparametric regression are presented in this book from a unifying, Bayesian perspective. Simulation-based full Bayesian Markov chain Monte Carlo (MCMC) inference, as well as empirical Bayes procedures closely related to penalized likelihood estimation and mixed models, are considered here. Throughout, the focus is on semiparametric regression and smoothing based on basis expansions of unknown functions and effects in combination with smoothness priors for the basis coefficients. Beginning with a review of basic methods for smoothing and mixed models, longitudinal data, spatial data and event history data are treated in separate chapters. Worked examples from various fields such as forestry, development economics, medicine and marketing are used to illustrate the statistical methods covered in this book. Most of these examples have been analysed using implementations in the Bayesian software, BayesX, and some with R Codes. These, as well as some of the data sets, are made publicly available on the website accompanying this book.