Constance Grewe was professor at the Universities of Chambéry, Caen and Strasbourg (1997 to 2011). She was in charge of several Research Departments, member of the academic Scientific Councils, between 2003 and 2006, a Vice-President in charge of research and spent a research stay at the MPI of Heidelberg.

In 2004 she was appointed judge of the Constitutional Court of Bosnia and Herzegovina by the President of the European Court of Human Rights. 

Her publications are related to Comparative Constitutional Law, German Constitutional Law and interactions between international, European and domestic law. She has obtained the Research Award of the Humboldt Foundation and the title of Doctor honoris causa of the University of Basel (Switzerland).

Her research project in Luxembourg concerns the constitutional courts with international participation.