Cold fusion is a hypothesized form of nuclear fusion that takes place at much lower temperatures than are traditionally though required.
In a nuclear fusion reaction nuclei of light elements join together (fuse) to produce heavier nuclei with a higher atomic number. The mass of these heavier nuclei is slightly less than the sum of the masses of the original nuclei and the missing mass is released as energy, in accordance with the famous equation E=mc².
For man-made fusion, the nuclei involved may be two deuterium (heavy hydrogen) nuclei, each consisting of one proton and one neutron and combining to produce a helium nucleus or alpha particle (two protons and two neutrons). Tritium is sometimes also used, but the distinction is not relevant to this article. Other forms of fusion are possible. With hot deuterium fusion, the product is only rarely helium, which is always accompanied by an energetic gamma ray. The vast bulk of such fusions result in a neutron plus Helium-3, or tritium plus a proton.
Since nuclei have a positive charge, they repel one another and thus the chief problem in achieving ordinary fusion is to get the nuclei close enough together to fuse. With hot fusion, this is accomplished by major heat, millions of degrees.
Cold fusion was given the name, popularly, because the discoverers of cold fusion claimed that the bulk of the heat they found was due to an "unknown nuclear reaction," and most observers thought that it must involve deuterium fusion. Yet the reaction did not produce copious neutrons or tritium, which would be easily detected, contradicting the idea that it was hot fusion somehow occurring under overall cold conditions.
High Temperature Fusion
The approach that has generally been taken is to heat the gaseous deuterium to such a high temperature that it becomes a plasma and that the nuclei have sufficient kinetic energy so that some of them can overcome their repulsion and collide.
However, the main problem of this approach is the containment of the high energy plasma. This may be achievable using precisely shaped magnetic fields, but to date the longest period of stable fusion under this mechanism has been around half a second.
Low Temperature Fusion
There is, however, no fundamental law that says that this high temperature approach is the only way to get the deuterium nuclei close enough to react, or that the only possible fusion reaction is between only two nuclei. Other approaches have been posited. For example, if the electrons of deuterium atoms could be persuaded to orbit much closer to the nucleus then the atom would have an overall neutral charge until it was in much closer proximity to another atom (i.e. until the nuclei were within the orbit of the electrons).
Quantum Theory indicates that this would be impossible with electrons, but it is known to occur with a muon instead of an electron. Since a muon is 207 times heavier than an electron it orbits 207 times closer. 
However, muon-catalyzed fusion requires the production of muons, which requires substantial energy, and while one muon may catalyze more than one fusion reaction, eventually the muons are captured by other nuclei, such as helium, and the muon cannot then cause more fusions. It is real, but far from practical for energy production, as far as any approach known.
In 1989, electrochemists Martin Fleischmann and Stanley Pons of the University of Utah claimed to have produced high levels of heat, and a low level of neutrons, loading a palladium cathode through electrolysis in heavy water, and some speculated that this might possibly become a source of cheap energy in the future.
After Fleischmann and Pons made their claim, a number of hasty attempts to replicate the effect failed, and the claim was generally discredited. However, work continued and Melvin Miles, at the United States Navy China Lake Research Laboratory, one of the original negative replicators, eventually confirmed excess heat, and so did others. Mike McKubre of Stanford Research International showed that a deuterium to palladium loading ratio of greater than 90% was needed to see the effect. The initial failures at MIT and Cal Tech used loading of well under 80%.
Miles later found that helium, in the Fleischmann-Pons Heat Effect, is produced with a ratio to the anomalous heat that is commensurate with the ratio expected from some form of deuterium fusion to helium (this ratio would be found with any reaction that starts with deuterium and ends with helium).
The field, still being actively researched, has been covered in many academic publications in recent years, including a featured review by Edmund Storms, "Status of cold fusion (2010)," in Naturwissenschaften, October 2010. The abstract of this review included:
- The evidence supports the claim that a nuclear reaction between deuterons to produce helium can occur in special materials without application of high energy. This reaction is found to produce clean energy at potentially useful levels without the harmful byproducts normally associated with a nuclear process.
Springer-Verlag is the second largest scientific publisher in the world, and Naturwissenschaften is their "flagship multidisciplinary journal," published since 1913. The appearance of this review in a mainstream peer-reviewed journal is a milestone in the recognition of cold fusion, after so many years of neglect.
Research is ongoing in many laboratories around the world.
The field has expanded from deuterium in palladium to also include hydrogen in nickel and nickel nano-powder, low energy glow discharge, and transmutation experiments (mostly in Japan). Research funding sources in the US include the Defense Advanced Research Projects Administration (DARPA), and the Department of Defense, Threat Reduction Agency.
There are also companies claiming to have working Nickel-Hydrogen demonstration devices, claiming power levels that could see commercial usage; however there is no open independent evidence that these devices work reliably, only enthusiasm, promises from the companies -- often not met --, and some public demonstrations that convinced some, but that were also flawed in ways that eventually led to extended skepticism even from those who have accepted cold fusion in general.
The 17th International Conference on Cold Fusion was held in Deajeon, Korea, August 12-17, 2012.
- Popular Science, November 2012. "Can Andrea Rossi's Infinite-Energy Black Box Power The World--Or Just Scam It?" The Rossi claims have not been independently confirmed, and publicly-available evidence is inadequate to determine if the devices work at all, and if they do, if they depend on cold fusion, or low-energy nuclear reactions, or not. There is minor coverage in this article of other, scientifically-established, approaches to cold fusion.
- Forbes, October 2012 "Cold Fusion Gets a Little More Real." Author Mark Gibbs doesn't clearly distinguish between scientific reality (established) and practical reality (not established).