Entry by land by bus, train or ship is unrestricted and possible for all citizens from all neighboring countries of Hungary without the obligation to test or quarantine.

For EU citizens a proof of a digital COVID certificate from the EU is required for entry by air and from countries outside the Schengen area.

Unrestricted entry is still possible for people with a vaccination certificate from the following countries with which Hungary has signed bilateral agreements for the mutual recognition of vaccination certificates: Albania, Bahrain, Georgia, Kazakhstan, Croatia, Morocco, Moldova, Mongolia, Montenegro, North Macedonia, Romania, Serbia, Turkey, Ukraine and Cyprus. Vaccination certificates from other countries are not accepted for entry.

Citizens from following countries can enter Hungary by air in case they have a negative PCR test not older as 72 hours:

• a Member State of the European Union or in a candidate country for membership of the European Union,
• a Member of the Organization for Economic Co-operation and Development,
• in a Member of the North Atlantic Treaty Organization, e.g. USA, Canada, Japan
• the Russian Federation,
• he People's Republic of China,
• the United Arab Emirates,
• the Kingdom of Bahrain,
• the Member States of the Cooperation Council of the Turkish-speaking States: the Republic of Azerbaijan, the Republic of Kazakhstan, the Kyrgyz Republic, the Republic of Turkey, the Republic of Uzbekistan, or..."

The new rules in English can be found here, on the website of the police:
http://www.police.hu/en/content/information-on-general-rules-of-border-crossing