There are a number of pressing problems mankind is facing today that could, at least in part, be resolved by space systems. These include capabilities for fast and far-reaching telecommunication, surveying of resources and climate, and sustaining global information networks, to name but a few. Not surprisingly, increasing efforts are now devoted to building a strong near-Earth satellite infrastructure, with plans to extend the sphere of active life to orbital space and, later, to the Moon and Mars if not further. The realization of these aspirations demands novel and more efficient means of propulsion. At present, it is not only the heavy launch systems that are fully reliant on thermodynamic principles for propulsion. Satellites and spacecraft still widely use gas-based thrusters or chemical engines as their primary means of propulsion. Nonetheless, similar to other transportation systems where the use of electrical platforms has expanded rapidly, space propulsion technologies are also experiencing a shift toward electric thrusters that do not feature the many limitations intrinsic to the thermodynamic systems. Most importantly, electric and plasma thrusters have a theoretical capacity to deliver virtually any impulse, the latter being ultimately limited by the speed of light. Rapid progress in the field driven by consolidated efforts from industry and academia has brought all-electric space systems closer to reality, yet there are still obstacles that need addressing before we can take full advantage of this promising family of propulsion technologies. In this paper, we briefly outline the most recent successes in the development of plasma-based space propulsion systems and present our view of future trends, opportunities, and challenges in this rapidly growing field.