I'm not very updated on random theories regarding the Altaic theory (which I personally am agnostic about; though I slant towards not believing in it due to the extreme lack of any regular sound change patterns from "Proto-Altaic") and the classification of Korean and Japanese, and English Wikipedia generally regards the consensus being that Japonic and Korean are isolates. However, the Chinese Wikipedia gives many, many theories, and the Japonic language family is also regarded as controversial (!) in many articles in CW. However, the Chinese Wikipedia is quite famous for not citing things properly and containing boatloads of "weasel words" in part due to common Chinese style abusing the word 据说 (it is said; according to some) a lot. This huge block from Chinese Wikipedia has very little footnotes, so I'd like some help on distinguishing viable theories from fringe or probable Wikipedia editor pet theories.
Here's a translation of the relevant parts from https://zh.wikipedia.org/wiki/阿尔泰语系 , with the original.
The classsification of Korean and Japanese (including Ryukyuan) has always been a focus for academic debate. There are generally speaking five camps:
如通古斯语(赫哲) Mini bithe-i 我的书 Bi mini bithe-we-i hvla-i.我读我的书。 bithe-we-i中的we是受格后缀，而i是第一人称领属后缀。hvla-i中的i为动词第一人称后缀。 [...]
The first camp believes that Korean and Japanese do belong to this [Altaic] family, which could only be true if the Macro-Altaic theory is true, because Korean and Japanese have some Altaic characteristics. (note: this sentence is equally awkward in the original)
Liquids do not appear in the first syllable of native words
Conjugation for person (however, J/K does not have this one)
[A typical Altaic languages] such as Tungusic (Nanai) Mini bithe-i "My book" Bi mini bithe-we-i hvla-i "I'm reading my book". (note: incomplete sentence in original) bithe-we-i's "we" is a patientive suffix, while "i" is a ferst person genitive (?) suffix. hvla-i's "i" is a first person conjugation for the verb.
The remaining three characteristics do belong to Japanese, giving this theory significant support. However, Japanese shares very little vocabulary with other Altaic languages, so scholars against this viewpoint take this as strong evidence against this view.
The second camp believes Japanese and Korean belong to a new [i.e. separate] language family. Scholars believing in this theory think that Japanese grammar is shockingly similar to that of Korean - both use SOV - and both have had strong influence from Old Chinese. Thus, some people believe that Japanese and Korean is a mixed language family arising from the creolization of Sino-Tibetan and Altaic. However, the lack of common vocabulary between Japanese and Korean also becomes a arguing point for dissenters.
The third camp believes Japanese and Ryūkyūan belongs to a new family, the Japonic family. Since Japanese and Ryūkyūan do have many similarities, this theory receives the support of some scholars, but remains controversial.
The fourth camp believes that Japanese and Korean are both isolates, unrelated to other languages of the world. Scholars believing in this view support it with the "lexical similarity problem".
The fifth camp believes that Japanese should belong in the Sino-Tibetan family under Tibeto-Burman. This theory is supported by a camp of Japanese scholars led by Nishida, who holds that Japanese word order is similar to that of Burmese, and also has vocabulary similar to those of Burmese and southern Chinese dialects; even the pitch accent has similarities with the tonal systems of these languages. However, other people believe that since Japan is very far from both Tibet and Burma and separated by Austronesian and Tungusic language areas, this theory should be ignored. However, yet others think that according to race migration history, around the Shang and Zhou dynasties of China, some dialects of Tibeto-Burman and Austronesian mixed, and [their speakers] used their advanced seafaring skills to migrate to Korea and Kyūshū under the pressure of the Sino-Tibetan speakers (Zhou dynasty). At that time, the Tungusics have yet to set up home in the eastern Mongolian plateau, so this theory is extremely probable.
Except the five above camps, some others believe Japnaese belong to Austronesian.