Eskildsen began his photographic career as an apprentice to the Danish Royal Photographer Rigmor Mydtskov. In 1994 he moved to Finland to study photographic book-making at the University of Art and Design in Helsinksi, graduating with an MA in photography in 1998.
As well as gallery exhibitions of his work, much of Eskildsen's output is in the form of books, often based on extensive travels throughout the world.
In 2000 he began an ambitious six-year project with the writer and poet Cia Rinne spending time with different communities of Roma people, Europe’s largest ethnic minority. The study documented their daily lives, living conditions and culture as well their experience of prejudice and marginalisation. The project took them to seven countries: Hungary, Romania, Greece, Russia, Finland, France and India. The result was published as the book ‘The Roma Journeys’ (2007) containing 400 photographs by Eskildsen accompanied by Rinne’s text which provides historical backgrounds as well as vivid personal insights into the lives of the subjects. The book also contains a foreword by Günther Grass and a CD with field recordings and music.