Robots are increasingly designed to physically interact with humans in unstructured environments, and as such must operate both accurately and safely. Leveraging compliant actuation, typically in the form of series elastic actuators (SEAs), can guarantee this required level of safety. To date, a number of frequency domain techniques have been proposed which yield effective SEA torque and impedance control; however, these methods are accompanied by undesirable stability constraints. In this research, we instead focus on a time domain approach to the control of SEAs, and adapt two existing control techniques for SEA platforms. First, a model reference adaptive controller is developed which requires no prior knowledge of system parameters and can specify desired closed-loop torque characteristics. Second, the time domain passivity approach is modified to control desired impedances in a manner that temporarily allows the SEA to passively render impedances greater than the actuator's intrinsic stiffness. This approach also provides conditions for passivity when augmenting any stable SEA torque controller with an arbitrary impedance. The resultant techniques are experimentally validated on a custom prototype SEA.