We present mlr3mbo, a modular toolbox for Bayesian optimization in R. mlr3mbo supports single- and multi-objective optimization, multi-point proposals, batch and asynchronous parallelization, and robust error handling. While it can be used for many standard Bayesian optimization variants in applied settings, researchers can also construct custom Bayesian optimization algorithms from its flexible building blocks. In addition to an introduction to the software, its design principles, and its building blocks, the paper presents two extensive empirical evaluations on the surrogate-based benchmark suite YAHPO Gym. To identify robust default configurations for both numeric and mixed-hierarchical optimization regimes, and to gain further insights into the respective impacts of individual settings, we run a coordinate descent search over the mlr3mbo configuration space and analyze its results. Furthermore, we benchmark mlr3mbo against a wide range of established optimizers, including HEBO, SMAC3, Ax, and Optuna, and find that it performs on par with state-of-the-art.