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Over the last decades, the challenges in applied regression and in predictive modeling have been changing considerably: (1) More flexible regression model specifications are needed as data sizes and available information are steadily increasing, consequently demanding for more powerful computing infrastructure. (2) Full probabilistic models by means of distributional regression - rather than predicting only some underlying individual quantities from the distributions such as means or expectations - is crucial in many applications. (3) Availability of Bayesian inference has gained in importance both as an appealing framework for regularizing or penalizing complex models and estimation therein as well as a natural alternative to classical frequentist inference. However, while there has been a lot of research on all three challenges and the development of corresponding software packages, a modular software implementation that allows to easily combine all three aspects has not yet been available for the general framework of distributional regression. To fill this gap, the R package bamlss is introduced for Bayesian additive models for location, scale, and shape (and beyond) - with the name reflecting the most important distributional quantities (among others) that can be modeled with the software. At the core of the package are algorithms for highly-efficient Bayesian estimation and inference that can be applied to generalized additive models or generalized additive models for location, scale, and shape, or more general distributional regression models. However, its building blocks are designed as "Lego bricks" encompassing various distributions (exponential family, Cox, joint models, etc.), regression terms (linear, splines, random effects, tensor products, spatial fields, etc.), and estimators (MCMC, backfitting, gradient boosting, lasso, etc.). It is demonstrated how these can be easily combined to make classical models more flexible or to create new custom models for specific modeling challenges.