With measures being lifted across Europe, countries have decided to release the strict border regime for incomers from foreign countries.
As a result, countries can now be visited also by people not vaccinated against Covid, who are not required to stay in quarantine. Some even dropped all entry requirements and do not check any certificates.
Still, it is good to check specific entry conditions before you travel to another country. One big help when travelling across the EU is the EU Digital Covid Certificate (or EU green pass), containing a QR code with information on vaccination, recovery from Covid, and Covid tests. They are often accepted as an alternative to other documents required when crossing borders.
A guide on how to obtain your EU green pass if you were vaccinated in Slovakia can be found here.
When coming to Slovakia from abroad, people need to fill in the eHranica online form and self-isolate, unless they have been fully vaccinated against Covid or recently recovered from the disease (with some exceptions).

The Slovak Spectator looked at the conditions for incomers applied by the neighbouring countries and also some countries overseas. (A complete list of conditions for entering the foreign countries can be found on the website of the Foreign Affairs Ministry, but in Slovak only.)