Professor Grewe earned her Bachelor’s degree in Frankfurt in 1996 and completed her studies in Law at the Faculty of Law in Caen, France in 1974. She earned her Ph.D. in 1979 at the University of Caen with a thesis on German cooperative federalism.  

She was a professor at the University of Chambéry from 1981 to 1983, a Professor at the University of Caen from 1983 to 1997, and a professor at the University in Strasbourg from 1997 to 2011. She was in charge of several research departments, and a member of the Scientific Councils of the University of Caen and the University of Strasbourg. She served as the Vice President from 2003 to 2006, in charge of the research. She published numerous books and articles in the field of Comparative Constitutional Law, German Constitutional Law and interactions between international, European and domestic law. She is also a member of the Editorial Advisory Board of the Law Journal EuGRZ (Europäische Grundrechte Zeitschrift) as well as of RFDC (Revue francaise de droit constitutionnel) and an expert in the Council of Europe. In 2008, she obtained the Research Award of the Humboldt Foundation and received the title of Doctor honoris causa from the University of Basel (Switzerland) in 2012.

She served as a Judge of the Constitutional Court of Bosnia and Herzegovina from May 2004  December 2016. She served as the Vice-President of the Constitutional Court of BiH from 2009 to 2012.