Hungary is one of the oldest nations of Europe, the first king of Hungary dating back to the year 1,000; back then it covered an area much larger than today, including the current Slovakia and Croatia. It was occupied by the Turks early in the 16th century and remained a province of the Ottoman Empire for nearly a century; at the end of the 17th century it was taken back by the Austrians so that the Emperor of Austria became also the King of Hungary; in 1867 Hungary was recognized as having parity with Austria, so that the empire became known as Austro-Hungarian, and the two cities of Buda and Pest were combined to form a new capital, Budapest, connected by a new cable suspension bridge. After the first world war Hungary became an independent republic and remained so even after the second world war.
The most noteworthy bike route is the Donauradweg which after Budapest touches upon the historic city of Esztergom, the city of Attila, and Györ, before reaching the border with Slovakia just before Bratislava.
At the time of my only visit of this route in 1995, the only section that was really cyclable was between Budapest and Esztergom; for the remainder I relied on small local roads for the most part far from the river, so that I could see the Danube only occasionally. Since then the situation must certainly be improved somewhat.
Again, in 1995, Budapest was hardly a bikable city; only on the island in the middle of the Danube were there any true bike paths; at Pest traffic was exceedingly heavy, a situation hardly conducive to cyclists.
Hungary is now part of the European Union but has not adopted the Euro as its currency. It is necessary therefore for travelers to exchange currency.