Denmark is open to tourists and quarantine is required unless vaccinated. Starting September 10th, Denmark will drop all mandates and restrictions regarding COVID.
Entry to Denmark depends on which country you’re coming from, using their traffic light system. Tourists are allowed to enter Denmark if they have an EU Digital COVID certificate, If they are resident in an EU or Schengen country you can enter Denmark if they are fully vaccinated, newly tested or recovered from COVID-19 (or previously infected). You can document this through your EU Digital COVID certificate or by other means of documentation. Fully vaccinated people are exempt from the requirements to be tested and isolate on arrival in Denmark unless they have been in a red country/region during the 10 days preceding their arrival. The Danish corona passport app is the Danish version of the EU’s Digital COVID Certificate which can be used in different countries. More info here
Denmark is the first country in Europe to lift all Covid measures and restrictions, starting on the 10th of September. Source