We present a summary of two round-table discussions held during two subsequent workshops in Montreal (Canada) on 16 April 2014 and Ostend (Belgium) on 8 July 2015. Five species of the genus Achomosphaera Evitt 1963 and 33 of the genus Spiniferites Mantell 1850 emend. Sarjeant 1970 occuring in Pliocene to modern sediments are listed and briefly described along with remarks made by workshop participants. In addition, several holotypes and topotypes are reillustrated. Three species previously assigned to Spiniferites are here considered/accepted as belonging to other genera: Impagidinium inaequalis (Wall and Dale in Wall et al. 1973) Londeix et al. 2009, Spiniferites? rubinus (Rossignol 1962 ex Rossignol 1964) Sarjeant 1970, and Thalassiphora balcanica Balteş 1971. This summary forms the basis for a set of papers that follows, where points raised during the workshops are explored in greater detail.