Permanent exhibitions in museums are the outcome of processes of construction of historical knowledge, which can occur both within or outside the museum. However, this particular type of historical narrative is somehow inconsistent with the possibility of integrating more recent academic work and it is physically limited when it comes to embrace the historical complexity and multilayered lives of objects. With examples taken both from art and science museums, we will seek to outline the problems and possible responses to curating history, especially when departing from a material culture approach or science studies at the same time as trying to integrate the public's voice. This paper is the second step in a project led by researchers from the EUI in Florence, the CHAM research centre in Lisbon and the University of Warwick which culminated with an international workshop in Florence in October 2017 (https://curatinghistory.wordpress.com/).