A spiral conveyor for positively driving a conveyor belt (20) along a helical path. The spiral conveyor includes a rotating cylindrical tower (10) with parallel drive members (14) extending from the bottom to the top of the tower on its periphery. Each drive member includes an outwardly protruding ridge (28) that varies in height from the bottom to the top of the tower. The variations in height facilitate the belt's entry onto and exit from the tower and robust, positive driving engagement with the inside edge of the belt along the majority of its path along the tower. In another version, a conveyor belt has teeth (62) with guide surfaces (78, 79) at the inside edge of the belt. The teeth guide the drive members between belt rows into driving engagement with drive faces at the inside edge of the belt.