In this paper, we identify some milestones in the construction process for mobile science museums and centres in Brazil. As background for presenting the Brazilian context, we initially address the records found on the earliest travelling museum exhibitions and mobile museums in Europe and North America. We then introduce the role of UNESCO in the promotion and implementation of travelling science exhibitions and museums in several countries. Finally, we document important events in the history of mobile science museum and centres in Brazil and outline three general and inter-related challenges currently faced by them.