For autonomous robots to operate in the open, dynamically changing world, they will need to be able to learn a robust set of skills from relatively little experience. This talk begins by introducing Grounded Simulation Learning as a way to bridge the so-called reality gap between simulators and the real world in order to enable transfer learning from simulation to a real robot. It then introduces two new algorithms for imitation learning from observation that enable a robot to mimic demonstrated skills from state-only trajectories, without any knowledge of the actions selected by the demonstrator. Connections to theoretical advances in off-policy reinforcement learning will be highlighted throughout. Grounded Simulation Learning has led to the fastest known stable walk on a widely used humanoid robot, and imitation learning from observation opens the possibility of robots learning from the vast trove of videos available online.