Cold Fusion was an hypothesis, and also a joke to ridicule the claims of nuclear energy production in hydrides, as Fleischmann&Pons first published, but also like what NASA GRC Fralick 89, shown during gas permeation in palladium. Fusion is not proven, since we don't know what happen.
LENR (low energy nuclear reaction) is a descriptive name for a phenomenon. It was invented to get way from negative connoted "cold fusion", and to avoid proposing an answer.
LENR as it is proven by hundreds of experiment, replicated by many team, even today, and proposed by few industrialist, is a nuclear phenomenon, which happen in Hydrides (hydrogen absorbed inside some transition metal like Pd Ni W Ti...). Phenomenon observed are heat production, production of He4 correlated with heat (Miles, ENEA Deninno), tritium (without heat), neutrons (but much less than hot fusion), heavy elements transmutation (Iwamura,Toyota...). For calorimetry different methods have been used, initially isoperibolic calorimetry, but also isothermal (McKubre), some explosions allowed to estimate heat (Biberian). Recently with less precision, some industrialist used radiometry (Elforsk), or multi-phase flow calorimetry (Defkalion, Rossi) to estimate kW of heat, at COP>3...
LENR in hydrides is in the family of the condensed matter effects, like semiconductors, superconductors. This explain why scattering statistics used in plasma physics cannot be used. The decades of research (as shows recent papers by ENEA ICCF18) shows that surface condition, impurities, crystallography are key parameters of the success, beside some more evident condition (current density, loading)... Today the cause of failures of pretended reference experiments justifying to deny LENR reality, are all known. most are simply basic reason (like for Caltech,MIT,Harwell experiments,w hou could not succeed even if they took time and used good calorimetry).
Today no theory explain LENR, but there are many direction and some incomplete theory proposed.
To allow LENR few mechanism are needed. it can be "collective behaviors" (like for superfluidity, LASER - group quantum entanglement ), electrostatic screening (like gold color is explained), quantum wave resonance, weak interaction intermediate (like electron-capture, inverse beta decay), use of condensed matter and surface pseudo-particle (plasmons, SPP, polaritons)... Most theories considered todays are based on classic quantum physics, using the classic subtleties of condensed matter quantum physics, between quantum effects and unusual dimensions or lattice/surface defects. For non specialist, there is no interest in trying to consider any particular theory, since non works. LENR is plagued by the non-aristotelian curse, of having huge evidences and no theory.
Some LENR reactors are currently developed with industrial.
Andrea Rossi develop E-cat which have been tested by swedish industry research consortium "Elforsk", who claimed success.
Defkalion develops Hyperion which have been tested more privately, with only one leaked report by Nelson, a NASA engineer working for a NGO.
Brillouin Corp have made test of their prototype with SRI.
Others company are preparing to develop another reactor, or application, or like National instruments just surf on that subject to develope their innovation image.
Despite many optimistic analysis, usual innovation experience propose that LENR will be industrial about 2016-2017...
Cognitive problems to accept LENR may delay that market entry, but it seems that in business circles, LENR can be discussed, provided nothing leaks.
You can find, beside many various documents and papers, an executive summary about all what is happening.
If someone find serious arguments against what I've gathered since 2 years as tech watcher, I am very much interested. For now, nothing seems to oppose that vision.
At worst, and probably, some industrial claims will be delayed few years because of technical problems.
At best all will be public in 1 year.