Support for radical parties on both the left and right is on the rise, fueling intuition that both radicalisms have similar underpinnings. Indeed, existing studies show that radical left and right voters have overlapping positions and preferences. In this article, however, we focus on the differences in the voting bases of such parties. We show that radical left and right voters have sharply diverging ideological profiles. When it comes to the historical traditions of the ‘left’ and ‘right’, these voters differ radically from each other. Both groups express the traditions associated with their mainstream counterparts—particularly with respect to (non-)egalitarian, (non-)altruistic, and (anti-)cosmopolitan values. Such differences also explain why radical left voters tend to be more, not less, educated than mainstream or radical right voters.