Cold fusion is a disputed physical effect that was first reported in 1989. It suggests that it may be possible to achieve room-temperature 'fusion' whereby energy is produced due to the fusion of atomic nuclei.
(It's called 'cold' because the alternative nuclear fusion techniques require Sun-like temperatures)
Despite a research spend of at least $15 million over three decades, there is still no agreement on whether or not the effect is real.
If it is real, there is also no agreement on the physics which could make it possible.
An extensive report can be found at Wikipedia