This package provides a flexible approach to Bayesian optimization / model based optimization building on the bbotk package. The mlr3mbo is a toolbox providing both ready-to-use optimization algorithms as well as their fundamental building blocks allowing for straightforward implementation of custom algorithms. Single- and multi-objective optimization is supported as well as mixed continuous, categorical and conditional search spaces. Moreover, using mlr3mbo for hyperparameter optimization of machine learning models within the mlr3 ecosystem is straightforward via mlr3tuning.