Taxonomy owes much to museums, and particularly to museums of natural history, because all the items accumulating in museum collections have to be identified before being organized into categories, whose relevance has to be established and whose boundaries have to be defined. This unleashes competition between different classification systems that mobilizes all of the institution’s resources and stokes interminable battles from which truth will eventually appear—which makes these systems an excellent object of study of taxonomic processes and issues. After a historical overview, we show how the principle of accumulation and the “systematic” scholarly classification of collections has become an obstacle to museum renovation and redesign to cater for “systemic” communication, which is more meaningful to the general public as it seeks to highlight common and obvious interactions between the different items on display.