Though they powered the Space Age, chemical rockets use fuel that is heavy, inefficient, and limited to the energy stored in chemical bonds. New propulsion systems are necessary if humanity wants to travel to deep space. NASA and space agencies around the world are looking towards fuel alternatives that are beginning to show promise: ion engines, solar sails, and nuclear fuel.
Ion engines work by accelerating charged atoms like xenon ions through a magnetic field and out the back of the spacecraft. The fuel is lightweight, and provides a low amount of thrust over a very long period of time, making it great for long-term deep-space exploration.
Another option is to eliminate onboard fuel all together and utilizing the sun to push the craft along with solar sails. Photons from the sun carry tiny amounts of momentum and an enormous sail in space could take advantage of the endless stream of photons from the sun, accelerating for as long as light is available.
The final, and perhaps most distant, proposal is the use of fusion and fission propulsion systems. Some scientists suggest using nuclear reactors to generate plasma that is then accelerated with a magnetic field, while others think hydrogen atoms could be forced together by lithium to generate small pulses of fusion.
The implementation of these ideas may be a long way off, but so are other planets -- and if we want to get to any of them, we'd prefer the journey be as fast as possible.