A little history...

Some background on the Magyar people
Originally, Buda and Pest were separate cities occupying the west and east banks of the river Duna (Donau/Danube). The Romas had a settlement there which was followed by a town. Parts of medieval Buda, including the Mathias Church, sit on a hill which was fortified in the 13th century by king Béla against invading Turks. When the Turks finally overran Hungary in the mid-1500's, they turned the church into a mosque. Not all of the 150 year occupation was a bummer for the Hungarians. When the Turks were ousted they left behind a series of naturally heated baths and ornate aribesque-like art. The next major occupation for Hungary came when it joined the Austrian empire in the 19th century. Maria Theresa's portrait is in many halls in Budapest! Many of the Neo-Gothic constructions and renovations date from this period, including the Mathias church re-model, the Fisherman's Bastion, Parliament, and the Chain Bridge (which connected Buda and Pest in 1849).
Unfortunately the dual-monarchy meant that Hungary was dragged into WW1. In 1919 it was its own state, which really didn't mean much to the Germans and Russians who rolled back and forth through the region 25 years later. Most of the major buildings and bridges have been re-built at least once as a result of the wars. Post-war Hungary set origionally had free elections, but the elected government formed a coalition with the Communists and were eventually edged out. Despite a revolution in 1956 the communist party ran Hungary until 1989, when the barbed wire fence separating Hungary from Austria was finally cut.