Crewe is the Director of the Centre for the Advancement of Scholarship atthe University of Pretoria, the former President of the Academy of Science of South Africa and former President of the Network of African Science Academies (NASAC). He obtained his bachelors and masters degrees at the University of Natal in Pietermaritzburg and his Ph.D in 1971 at the University of Georgia. He was Director of the Communication Biology Research Group at the University of the Witwaterstand and is currently the leader of the Social Insects Research Group at the University of Pretoria. He is a Fellow of the Royal Entomological Society of London, a Fellow of the Royal Society of South Africa, a founding member of the Academy of Science of South Africa, and received the Gold Medal of the Zoological Society of South Africa and the Ordre National du Mérite with the rank of Chevalier in 2006 from the French Government.  Fellow of the Academy of Science of the Developing World (TWAS), elected 2009 –Section   - Biological Systems and Organisms.

His research interests are in Behavioural ecology, social behaviour, chemical ecology, social organization in honey bees.