The idea, that it might be possible to artificially establish a nuclear fusion reaction away from a very high temperatures and pressures condition (within a burning star for instance), has initially been started in 1989 by the Fleischmann-Pons-Experiment. Fleischmann called the assumed fusion energy "Cold Fusion".
Now, nearly 30 years later, a lot of further research into this matter has been performed. Meanwhile, this field of research is now called "Solid-State Nuclear Fusion", "Condensed Matter Nuclear Fusion" or "Low Energy Nuclear Reaction", last but not least to distinguish from Fleischmann and Pons, who may or may not have an error in their experiment. Among the publications in this topic there are especially these ones:
Svenn Olafsson, Leif Holmlid, "Rydberg phases of Hydrogen and low energy nuclear reactions", at American Physical Society April Meeting, 2016.
Lawrence Forsley, Pamela Ann Ross, "Condensed Matter Nuclear Science Using Pd/D Co-Deposition", 2015.
V.F. Zelensky, "Nuclear Processes in Deuterium/Natural Hydrogen - Metal Systems", 2013.
Mae-Wan Ho, "From cold Fusion to Condensed Matter Nuclear Science - Evidence for cold fusion accumulates as enthusiasts transform it into a new discipline. Cheap, clean and safe nuclear energy one the horizon", 2007.
Edmund Storms, "A Student’s Guide to Cold Fusion", updated 2012.
Further, there are two commercial nuclear fusion applications by Lockheed-Martin and Boeing already:
Lockheed Martin has announced a compact nuclear fusion reactor to power huge aircraft carriers in 2018.
Lockheed Martin Compact Fusion Reactor Wikipedia Article.
Boing has patented a nuclear fusion drive in 2013, which has been published in 2015.
So, what is current research state in solid-state nuclear fusion? (Can we expect fusion reactors for power-plants and fusion drives for space ships in the near future?)