Understanding randomness is essential for modern life, as it underpins decisions under uncertainty. It is also an essential part of both the mathematics and science curricula in schools. Yet, research has shown that many people consider randomness difficult to perceive and argue about, with a number of different and contradictory views on the nature of randomness prevailing. This study explores beginning mathematics and science teachers' understanding of randomness. A questionnaire was used with student teachers in an initial teacher-education course to explore their understanding of and reasoning about randomness and random events. Results suggest that mathematics and science student teachers conceptualize and argue about randomness in a variety of ways. Furthermore, these different conceptualizations affect how they respond to both common classroom tasks and everyday contexts involving randomness. This raises important implications for the education of teachers who will themselves be teaching probability and statistical inference.