Updated rules of entering the Russian Federation, dd. 04 May 2021

Due to the coronavirus pandemic the government of the Russian Federation introduced restrictions and strict ban on the entry of foreign citizens into Russia since March 16, 2020 by the Order of  No. 635-r.
Because the situation is slowly improving, some restrictions have been lifted. Up to date international flights with some countries have been resumed, so foreign citizens from following countries are allowed to fly to Russia (the land borders of Russia remain closed):
 
Armenia
Azerbaijan
Cuba
Ethiopia
Finland
Germany
Greece
India
Japan
Kazakhstan
Kyrgyzstan
Maldives
Qatar
Serbia
Seychelles
Singapore
Sri Lanka
Switzerland
Syria
Tajikistan
Tanzania
The Republic of Korea
Turkey
United Arab Emirates
Uzbekistan
Venezuela
Vietnam 

Foreign citizens arriving to Russia must present negative PCR test done no later than 72 hours before arrival and entry to Russia. The certificate itself must be in English or translated in Russian. The plane bordering without the certificate is prohibited. Citizens of the Russian Federation returning to the country are allowed to take a PCR test at the airport upon arrival.
Usual visa requirements apply for the citizens of the list above. However, it should be noted it is not yet possible to obtain an electronic visa. Electronic visas are temporary not issued any more.  Ministry of Foreign Affairs recommends to track the news.
Citizens of other countries can enter Russia only for good and valid reasons, namely:
-    burial of a close relative
-    family reunification
-    medical treatment in the Russian Federation
-    employment of a highly qualified specialist
-    transit that does not require leaving the airport
-    permanent stay in the Russian Federation.

Due to the "British" COVID strain foreign citizens from the UK and Northern Ireland need to self-isolate upon arrival for two weeks. The others must not self-isolate. 
Foto: Global Look Press