By actual developments, we will inform you about the measures against the Corona Virus in Hungary.
  UPDATE May 1st 2021
UPDATE Mai 1st 2020: The third wave is slowly subsiding, the number of sick and dead people is still at the highs of top of the second wave. With thousands of new infections every day and a total of around 28,000 deaths, more people died in relation to the population at the end of April than in any other country in the world. The hospitals are still overloaded. Despite this, the government has partially reopened public life.
Allshops and services and outdoor catering are allowed to open. Public services remain strictly limited to actions that cannot be postponed. Schools and kindergartens are partially closed. Everyone has to wear a medical mask everywhere outside of their own home, with the exception of sporting activities, eating, drinking and staying outside of built-up areas. At night there is a curfew between 0:00 and 5:00 a.m. Of course, the rules on distance and hygiene still apply.
Anyone who has a Hungarian immunity certificate, i.e. lives in Hungary, has been vaccinated here or is considered to have recovered has further rights from May 1, 2021. They are allowed to stay overnight in hotels, to visit restaurants indoor, and to visit leisure and cultural facilities such as theatres, cinemas, museums, public baths or libraries. Sports facilities and sporting events are open to this target group. There is an exception to the wearing of masks in leisure and cultural facilities and sports facilities for everyone who has an immunity card. Hungarian citizens receive the ID automatically, foreigners living in Hungary upon request. Anyone who has been vaccinated abroad or has recovered from Covid 19 receives neither an immunity certificate nor the associated relief.
Anyone who violates the restrictions must expect severe fines, which can amount up to 1,000,000 Ft.
UPDATE March 10th 2021: Hungary continues to keep its borders closed. Citizens from Poland, Slovakia and the Czech Republic are exempted, they are allowed to enter the country with a negative test result that is not older than five days.
Hungarians and anyone, who has a registered or permanent residence in Hungary and can prove these facts by means of Hungarian documents (e.g. registration card with address card, permanent residence card with address card), as well as their family members, are also allowed to enter. Quarantine is ordered for each of these travellers.
Anyone who shows symptoms at the border is quarantined in a state facility, whoever shows no symptoms has to be quarantined at home for 10 days, an order is not required. Anyone who has not been checked at the border must report to the authorities. The police checks compliance with the quarantine several times a day. The quarantine at home can be shortened by two negative PCR tests, which must be taken at least five days apart; the costs are borne by the traveller. Foreign test results are only recognised as the first test if they come from a laboratory in a Schengen member state, the USA and Canada and are issued in Hungarian or English. Antigen tests (rapid tests, self-tests, etc.) are not recognised. Anyone who can officially prove that they have survived a corona infection in the last six months may enter the country without quarantine or a test.
Furthermore, exemption permits for business travellers from several countries, for the purpose of travel to judicial and official investigations or the participation in sport events can be granted within a narrow framework. The permit must be issued by the national police before departure.
Citizens of neighbouring countries and Hungarians living in neighbouring countries are allowed to commute to Hungary without quarantine, the same applies to Hungarians who commute to neighbouring countries. This rule does not apply to foreigners living in neighbouring countries.
Movement of goods and transit traffic are possible, but also subject to strict conditions.
DEPARTURESfrom Hungary are always possible from the Hungarian point of view, provided that the destination country does not prohibit entry. More and more countries see travelling to Hungary as a risk, some expressly warn. To the best of our knowledge Austria, Belgium, Germany, the Netherlands, and all parts of the United Kingdom have classified all of Hungary as a high-risk area, and since March 5, 2021, Germany has even classified it as a highest-risk area. At the Austrian border a negative PCR test (not older than 48 hours) must be shown, also for transit only! According to the respective regulations, every traveller must on return inform the relevant authorities and go in quarantine or be tested. As far as we know Switzerland hasn't classified Hungary as high-risk area. This information does not mean that countries not mentioned have not classified Hungary or parts of it as a high-risk area! 
These measures can be changed at any time, the list is not complete and does not constitute legal advice about what is allowed and what is not. 
Stay healthy or if you get this wish too late we wish you a speedy recovery!