Aðalheiður was a postdoctoral fellow at the Árni Magnússon Institute, funded by the Icelandic Centre for Research, from 2005 to 2007, a Sigurður Nordal research fellow at the same institute from 2008 to 2009, adjunct lecturer in folkloristics at the University of Iceland from 2009 and a senior lecturer in the same subject from 2012 to 2015.

[3] Aðalheiður's main focuses in teaching and research are medieval Norse literature, legendary sagas, folktales, folk ballads and rímur (metrical romances), the history of dance and the history of magic.

The saga was adapted for the stage in Hafnarfjörður Theatre by the company Annað svið in 2004 and the opportunity was taken to record the rímur (metrical verses) and publish them on CD along with Aðalheiður's edition of the text, with explanatory notes.

[4][5] In 2016 she was awarded the Dag Strömbäck Prize by the Royal Gustavus Adolphus Academy in Uppsala for her achievements in the field of Norse studies and folkloristics.

Aðalheiður has published short stories and poems and has won prizes for her writing.