These regulations are not very different from the rules of other European countries. It is, for example, forbidden to bring guns in or through the country. Certain types of food are also forbidden to import or export. You may carry and take HUF and other convertible currencies out of the country without any restriction of denomination value. (If the value of the currency brought in or taken out through the external border of the European Union exceeds the limit of EUR 10,000, this must be declared at the customs office.)
Further information on EU Cash Controls: https://taxation-customs.ec.europa.eu/customs-4/prohibitions-and-restrictions/eu-cash-controls_en
Every Hungarian Embassy can inform you about these rules, or you can request the help of a customs office once you are already in the country.
1054 Budapest, Széchenyi u. 2.
Phone: +36 1 428 5100
https://nav.gov.hu/en