It all started in 1989, when two chemists at the University of Utah named Stanley Pons and Martin Fleischmann believed they had succeeded in producing nuclear fusion in a jar. Hundreds of researchers all over the world scurried to reproduce the experiments, and failed.
By the end of that year, a panel of experts had conducted a Department of Energy (DOE) review and concluded there was no basis for the claims.
Fifteen years later, the DOE decided to take another look at the accumulated evidence over the last 15 years and re-evaluate the cold fusion controversy. They still didn't find the evidence sufficiently convincing to launch a federally-funded research program.
But they felt that funding agencies should consider proposed projects on a case-by-case basis, provided those proposals met "accepted scientific standards and undergo the rigors of peer review." Heck, sometimes long shots pay off, so why not throw some funding scraps into the hat? That's why there are a couple of research programs looking into cold fusion, most notably one with the US Navy's Space and Naval Warfare Systems (SPAWAR).
In 2009, SPAWAR claimed to have detected a cold fusion reaction, and there have a been few other promising glimmers here and there over the years. But robust reproducibility remains elusive, adding credence to criticisms from physicists that the much-touted results are likely to be due to experimental error (either in the set-up, or the measurements).
So, while physicists are willing to concede there might be something of marginal interest going on, most remain unconvinced that this is bona fide cold fusion. Hardly anyone holds out any hope of it becoming a viable energy source in the foreseeable future.
Oh, and we don't call it "cold fusion" anymore. The current preferred terminology is Low Energy Nuclear Reactions (LENR), thank you very much.