The reliable prediction of turbulent flows is of crucial importance since turbulence is prevalent in the majority of flows found in science and engineering. Turbulence is a multi-scale phenomenon, for which flow features can span several orders of magnitude in size. This results in enormous resolution requirements in numerical simulations of turbulent flow. The framework of large eddy simulation relaxes these resolution demands by resolving only the largest, most energetic features of the flow and approximating the dynamics of the smaller, unresolved scales with turbulence models. The goal of this thesis is to leverage the recent advances in machine learning methods to formulate data-driven modeling strategies for implicitly filtered large eddy simulation. To this end, two modeling strategies are devised based on the supervised and the reinforcement learning paradigms. First, artificial neural networks are trained using supervised learning to recover the unknown closure terms from the filtered flow field. It is demonstrated that recurrent neural networks can predict the unknown closure terms with excellent accuracy. The second modeling strategy is based on the reinforcement learning paradigm. For this, Relexi is introduced as a novel reinforcement learning framework that allows to employ legacy flow solvers as training environments at scale. With Relexi, artificial neural networks are trained within forced homogeneous isotropic turbulence to adapt the parameters of traditional turbulence models dynamically in space and time. The trained models provide accurate and stable simulations and generalize well to other resolutions and higher Reynolds numbers. It is demonstrated within this thesis that machine learning methods can be applied to derive data-driven turbulence models for implicitly filtered large eddy simulation and that these models can be trained and incorporated efficiently into practical simulations on high-performance computing systems.