You are a cross-border commuter (also known as a frontier worker) if you live in another EU/EEA country and work in Denmark.
There are several definitions, so please note that the term “cross-border commuter” may mean something different in another context, for example with respect to tax law.
Most cross-border commuters in Denmark are from Sweden, Germany and Poland.
More information on being a cross-border commuter from Sweden is available at the website of the Danish-Swedish information center, Oresunddirekt.
Info for cross-border commuters from Germany is available at a website by the Danish-German border region Sønderjylland–Schleswig and at a joint website, Eures Kompas, by Jobcenter Aabenraa and Agentur für Arbeit in Flensburg.