I recently learned they are unlikely linked to The Huns, so where did they come from?
Due to there not being any written Hungarian primary sources prior to the 10th century the origin of the Hungarians before they arrived in Hungary is difficult to determine. Therefore the analysis of the origins of the Hungarians relies heavily on archaeology and analysing modern day languages to determine if they have a common origin. While this method of analysis is mostly reliable, there is a chance that our understanding of Hungarian pre-history might be inaccurate.
The Hungarian language is an Ugric language, the Ugric language originated during the 3rd millennium BC when some of the Uralic people intermixed with members of an Indo-European language group (probably Iranian). The Ugric were also influenced by the Andronovo people.
Hungarians seem to have become a separate group from the rest of the Ugric people in 800 BC. They spent the next 1000 years as one of the various nomadic groups in the Eurasian steppes. Possibly near the Kama and Volga rivers in modern day Russia.
Eventually during the 5th century a large number of Hungarians settled in Perm Krai. During the 8th century some of these Hungarians moved to the Don river and became vassals of the Khazar Khanate. Due to a civil war in the Khazar Khanate many Hungarians migrated west. The first written mention of the Hungarians is from 831 when they were hired by the Bulgars to fight against the Byzantines.
The Hungarians then settled in some lands near Hungary known as Etelkoz (we're not sure where Etelkoz is).
The Hungarians started launching raids into modern day Hungary in 892 while allied with Arnulf King of East Francia (Also known as Arnulf of Carinthia). In 892 the territory of Hungary was ruled by Moravia. Moravia ceased to exist in the early 10th century.
After failed invasions of Italy and Bavaria and the end of their alliance with East Francia, the Hungarians settled in Hungary. The Hungarians continued to launch raids throughout Europe until they were converted to Christianity in 1001 be King Stephen I. After their conversion to Christianity Hungary developed a relatively more peaceful relationship with it's neighbours.