Zygophyseter varolai, a new genus and species of Physeteroidea (Cetacea, Odontoceti), is based on an almost complete skeleton from the Late Miocene (Tortonian) in southern Italy. The extreme elongation of the zygomatic process of the squamosal and the circular supracranial basin (probably for housing the spermaceti organ) delimited by a peculiar anterior projection of the supraorbital process of the right maxilla are the most distinctive features of this bizarre sperm whale. Large body size, large teeth present in both lower and upper jaw, and anteroposteriorly elongated temporal fossa and zygomatic process of the squamosal indicate that this cetacean (for which we suggest the English common name killer sperm whale) was an active predator adapted to feeding on large prey, similarly to the extant killer whale (Orcinus orca). A phylogenetic analysis reveals that Zygophyseter belongs to a Middle–Late Miocene clade of basal physeteroids, together with Naganocetus (new genus for the type of ‘Scaldicetus’shigensis). Moreover, the phylogenetic analysis shows evidence of a wide physeteroid radiation during the Miocene and that the extant Physeter and Kogia belong to two distinct families that form a clade representing the crown-group Physeteroidea. © 2006 The Linnean Society of London, Zoological Journal of the Linnean Society, 2006, 148, 103–131.