Optimal control has seen many success stories over the past decades. However, when it comes to autonomous systems in open-ended settings, we require methods that allow for automatic learning from data. Reinforcement learning is a principled mathematical framework for autonomous learning of good control strategies from trial and error. Unfortunately, reinforcement learning suffers from data inefficieny, i.e., the learning system often requires collecting much data before learning anything useful. This extensive data collection is usually not practical when working with mechanical systems, such as robots. In this talk, I will outline two approaches toward data-efficient reinforcement learning, and I will draw connections to the optimal control setting. First, I will detail a model-based reinforcement learning method, which exploits probabilistic models for fast learning. Second, I will discuss a model-predictive control approach with learned models, which allows us to provide some theoretical guarantees. Finally, I will discuss some ideas that allow us to learn good predictive machine learning models that obey the laws of physics. This geometric approach finds physically meaningful representations of high-dimensional time-series data. With this, we can learn long-term predictive models from a few tens of image observations.