There are various alternative speculations about the origins of the Hungarian language, even fanciful ideas about Hungarian being derived from the Sumerian language, but these are dismissed by linguists owing to a lack of evidence:
~ Hungarian has often been claimed to be related to Hunnish, since
Hungarian legends and histories show close ties between the two peoples.
Some people believe that the Székely, a part of the Hungarians living
in Romania, are descended from the Huns. However, the link with Hunnish
is uncertain, and it is not even known which languages the Huns spoke.
~ For many years (from 1869), it was matter of dispute whether Hungarian was a Finno-Ugric language, or was more closely related to the Turkic languages, a controversy known as the "Ugric-Turkish war". It is only in the discipline of linguistics that the victory of the Finno-Ugrists can be described as more or less complete, due to the evidence of the languages themselves.
However, the origin of a language is not necessarily equivalent to the genetic origin of the people which speak it, as for example can be seen with the Turkic-speaking Azeris, who are genetically kin to the Armenians. Regular sound changes that can be shown between corresponding elements of the basic vocabulary of Hungarian and other Uralic languages provide sufficient evidence to conclude that the languages are related. But while the language is clearly Finno-Ugric, the Hungarian people show more genetic similarities to people (such as Germans, Slavs, and Turks) who are closer to them geographically than the Finns, who in turn are more genetically similar to their Scandinavian neighbors than to the Hungarians. Such influences occur whenever people marry their neighbors, and as yet genetics has had little to say about the historical origins of the Hungarian people. The Finns, for example, are a poor example of the Finnic peoples genetically, for they seem to be predominantly Scandinavian in origin. A better genetic comparison for Hungarian would be with other Finnic peoples.
Regardless, there are noticeable Turkic influences in the Hungarian language. It appears that the Hungarians took over animal breeding from the Turkic Chuvash, and they were neighbors for many centuries, as a high proportion of words specific to agriculture and livestock are of Chuvash origin. There was also a strong Chuvash influence in burial customs. And all the Ugric languages, not just Hungarian, have Turkic loanwords related to horse riding.
As for the Huns, they were a large, loose grouping of tribes, who joined together at different points in their migrations. It may well be that the Huns of Asia met up with the Hungarians in the course of their long migration westward. At any rate, the Huns were defeated in the West in 451. Some then settled in the region that is now Hungary, but long before the migrations that brought the Hungarian people to the area.
As Finno-Ugrist scientists say, for this purpose no extra-linguistic (i.e. no empiric) evidence is needed, and the Finno-Ugrian theory is supported by what linguistics knows about related languages in general and could only be refuted if all other established language relationships were refuted at the same time. Other scientists dealing with the origin of Hungarian language (historians, linguists) regard these opinions as simplification.
~ The Hungarian language goes far back. It developed in a very particular manner and its structure reaches back to times, when most of the now spoken European languages did not even exist. It is a language which developed steadily and firmly in itself, and in which there is logic and mathematics with the adaptability and malleability of strength and chords. The Englishmen should be proud that his language indicates an epic of human history. One can show forth its origin; and alien layers can be distinguished in it, which gathered together during the contacts with different nations. Whereas the Hungarian language is like a rubble-stone; consisting of only one piece, on which the storms of time left not a scratch. It's not a calendar that adjusts to the changes of the ages. It needs no one, it doesn't borrow, does no buckstering, and doesn't give or take from anyone. This language is the oldest and most glorious monument of a national sovereignty and a mental independence. What scholars cannot solve, they ignore. In philosophy it's the same way as archeology. The floors of the old Egyptian temples, which were made out of only one rock, can't be explained. No one knows where they came from, or from which mountain the wonderous mass was taken. How they were transported and lifted to the top of the temples. The genuineness of the Hungarian language is a phenomenon much more wonderous than this. He who solves it shall be analyzing the Divine secret; in fact the first thesis of this secret: “In the beginning there was Word, and the Word was with God, and the Word was God.”
But by this time, of course, the modern understanding of Hungarian origins was already well understood.