Brekke has his doctorate in sociology from the University of Oslo. In his research, his main area of interest is migration research, and issues related to this such as: How is the asylum policy in this area developed? How do these conditions influence the experience of the individuals that arrive? And how are asylum seekers, refugees and immigrants integrated on the labour market?
His research contributions also include studies on the workings of the civil society and the conditions for voluntary activity – among others in a study of challenges the alternative culture of snowboarders represent to the established central organization for sports in Norway. He also holds an interest for ethnomethodology and social science methodology. Here he has published work on the use of photography as part of data-gathering among sensitive informants, and the use of interpreters in qualitative interviews.
Brekke is currently studying the political impact of the refugee situation that culminated in 2015. He is frequently used as a commentator in the media.