Brynhildur is an associate professor of Environment and Natural Resources at the University of Iceland, and is the Director of the Graduate Program in Environment and Natural Resources. Dr. Davidsdottir also is an advisor to the Icelandic government in issues of climate change mitigation and adaptation and is the appointed chair of the government committee that oversees greenhouse gas mitigation in Iceland. Before joining the University of Iceland in 2006, Dr Davidsdottir was an associate at Abt Associates Inc., Cambridge, Massachusetts, a lecturer at Boston University and a senior research associate at University of Maryland, College Park.

Much of her research has focused on; complex systems modelling of resource and environmental policy issues, such as regional responses within the United States to various climate change policy options and the impact of those responses on the natural environment; analysis of adaptation and mitigation options in the context of climate change; the dynamics of technological change towards a low carbon future; classifying and valuing ecosystem services; and the development of Sustainable Energy Development Indexes in several different contexts