The Ordovician biodiversification is considered one of the most significant radiations in the marine ecosystems of the entire Phanerozoic. Originally recognized as the ‘Ordovician Radiation’, a label retained during most of the 1980s and 1990s, the term ‘Great Ordovician Biodiversification Event’ (GOBE) was coined in the late 1990s and was subsequently adopted by most of the scientific community. The Ordovician biodiversification, has always been considered as a long-term adaptive radiation, resulting in the sum of the different individual diversifications of all groups of marine organisms that occurred diachronously during the entire Ordovician. More recently, based on different palaeontological datasets, comprising data from different palaeogeographical areas, the Ordovician radiation has been interpreted to occur at different times in different places. This is most probably related to the palaeogeography of the Ordovician, when the major palaeocontinents were variously located in low latitudes to develop biodiversity ‘hotspots’ during different time intervals. In particular, some authors, using the potentially biased dataset of the Paleobiology Database (PBDB), have considered the GOBE to be an early Middle Ordovician global bio-event. Accordingly, the GOBE thus apparently corresponds to a relatively short time interval, with dramatic diversity fluctuations resulting in a profound change in marine environments at a global scale, visible by a major pulse in biodiversification of all fossil groups around the world. A critical analysis of the published biodiversity curves and of our own data confirm the traditional view; the Ordovician radiation is a complex, long-term process of multiple biodiversifications of marine organisms. Rapid increases in diversity can be identified for some fossil groups, at regional or palaeocontinental levels, in particular within limited datasets. However, a short, dramatic event that triggered major biodiversity pulses of all fossil groups at a global level at a particular time interval is an oversimplification.