Our review on droplet dynamics in non-equilibrium systems has been published by Reports on Progress in Physics. Together with Frank Jülicher, Christoph Weber, and Chiu Fan Lee, we summarized the new theoretical developments in this exciting field of active matter. The review provides a thorough discussion of the thermodynamics of passive droplets and the extensions necessary to incorporate active processes. In particular, we discuss interesting phenomena that would not be possible in passive systems. Among these are the positioning of droplets, the control of droplet size, the stabilization of emulsions, and spontaneous division. All these effects rely on active processes that modify normal droplet dynamics, where for instance surface tension ensures a spherical shape. Such active droplets can for instance be observed in the non-equilibrium environments of biological cells. The review also provides the basis for extending the theory to more complex situations, which surely will unravel novel dynamical phenomena of active emulsions. These processes will help us to better understand biological systems and might also be applicable in technical applications.