The museum is an inventive, globally and locallytranslated form, no longer anchored to its modernorigins in Europe. Contemporary curatorial work, inthese excessive times of decolonisation andglobalisation, by engaging with discrepanttemporalities – not resisting, or homogenising,their inescapable friction – has the potential toopen up common-sense, ‘given’ histories. It does sounder serious constraints – a push and pull ofmaterial forces and ideological legacies it cannotevade. This chapter explores the ‘times’ of thecurator, in terms of both these times we live in, inwhich curatorial theory and practice seem to beever-present, and a sense of the curator’s task asenmeshed in multiple, overlapping, sometimesconflicting times. It is concerned primarily withthe later, the discrepant temporalities, or perhapsthat should be ‘histories’, or even ‘futures’, thatare integral to the task of the curator today. Incontrast to the history of museum curating,curatorial work in recent years has been transformedby the re-emergence of indigenous cultures in formersettler colonies which suggest the decentring of theWest. Drawing on research in the USA, Canada and thePacific Islands, and analysing several diverse casestudies and examples, the chapter explores examplesof ‘indigenous curating’, that is to say, workingwith things and relations in transforming times. Indoing so, it contributes to a world-wide debate,which this book is part of, about museums and thefuture of curatorship.