In 1991, the year he graduated, Grarup won the Danish Press Photographer of the Year award, a prize he would receive on several further occasions. In 1993, he moved to Berlin for a year, working as a freelance photographer for Danish newspapers and magazines.

During his career, Grarup has covered many wars and conflicts around the world including the Gulf War, the Rwandan genocide, the Siege of Sarajevo and the Palestinian uprising against Israel in 2000. His coverage of the conflict between Palestine and Israel gave rise to two series: The Boys of Ramallah, which also earned him the Pictures of the Year International World Understanding Award in 2002, followed by The Boys from Hebron.

His book, Shadowland (2006), presents his work during the 12 years he spent in Kashmir, Sierra Leone, Chechnya, Rwanda, Kosovo, Slovakia, Ramallah, Hebron, Iraq, Iran, and Darfur. In the words of Foto8's review, it is "intensely personal, deeply felt, and immaculately composed."His second book, Darfur: A Silent Genocide, was published in 2009 and his enormous AND THEN THERE WAS SILENCE was published in 2017

Per Folkver, Picture Editor in Chief of the Copenhagen daily Politiken, where Grarup has worked, has said of Grarup that "He is concerned about what he is seeing and doing longer stories and returning to the same places."

After leaving his post at Politiken in the autumn of 2009, he joined the small Danish photographic firm Das Büro in January 2010 where he concentrated on the national market. He continues his international work with NOOR photo agency in Amsterdam, of which he is a cofounder.

1991: Picture of the year, Denmark. 1st. prize – Photographer of the year
1995: Picture of the year, Denmark. 1st. prize – Photographer of the year
2000: Picture of the year, Denmark. 1st. prize – Photographer of the year
2001: World Press Photo – 1st. prize, People in the news – stories
2001: UNICEF – Children photo of the Year. Jury's Special Award.
2001: Visa pour l'Image – VISA D`Or – Finalist.
2002: World Press Photo – 1st. prize, People in the news – stories
2002: Pictures of the Year International World Understanding Award
2002: Finalist, W. Eugene Smith Memorial Fund for Humanistic Photography, New York.
2002: UNICEF Children photo of the year award. 1st. Prize[15]
2003: Picture of the year, Denmark.
2003: Feature Story of the Year, Denmark.
2004: Picture of the year, Denmark. 1st. prize – Photographer of the year
2005: Visa d'or.
2008: Picture of the year, Denmark. 1st. prize – Photographer of the year
2011: Leica Oskar Barnack Award winner.
2013: I Shot It, 1st prize, Black and White 2nd Quarter 2012.
2013: World Press Photo, 1st prize stories, Sports Feature.