Already on the Drawing Board
Bombs as Fuel
One of the earliest ideas for interstellar travel comes from the 1958 Project Orion, which proposed that a vessel could travel to different stars using nuclear bombs as its fuel. A craft would drop about five bombs every second, whose detonations would propel it forward. Initially, this idea was proposed for a ship traveling to Mars. In the 1970s, the British Interplanetary Society revised the idea to create its Project Deadalus. This hypothetical craft would use fusion explosions to propel it past Barnard's star, a six light year trip, in about 50 years. Unfortunately for NASA researchers, the Nuclear Test Ban Treaty forbids the explosion of nuclear weapons in the Earth's atmosphere and developing a bomb-based ship would be illegal.
In the 1960s, the physicist Robert Bussard proposed a craft that would pick up fuel in space rather than carry its own. The Bussard Interstellar Ramjet is a hypothetical vehicle that would collect stray protons that exist in interstellar space with a magnetic scoop and somehow create fusion reactions that would propel the craft. This craft would work in theory, but there are still many problems that would have to be overcome: drag created by the scoop, how many protons can be scooped, much less somehow getting them to fuse.
When light strikes an object, it pushes on that object with a very small smount of force. If you use large amounts of light on a large surface, that force becomes noticeable. Robert Forward's proposed light sail works on this concept. A thousand-ton vehicle with a crew could make it to the nearest star in 10 years with a thousand kilometer sail and a 10-million-gigawatt laser. This sounds pretty simple until you realise that 10-million-gigawatts is 10,000 times the amount of power used on the entire Earth today. This technology requires a massive leap forward in creating energy before it can become viable.