This dissertation examines the rotational (or attitude) dynamics of variable mass systems. In the context of this study, a variable mass system comprises a rigid base and a fluid phase delimited by a massless porous shell. The mass variability is accounted for by allowing the rigid part to be consumable and the fluid phase to enter and/or exit the region of interest through the shell. The document begins by providing a brief historical perspective on the developments in attitude dynamics of variable mass systems, a relatively young field in the context of classical mechanics, mostly motivated by interest in spaceflight. This introduction is followed by examinations of general variable mass systems and proceeds onto torque-free variable mass cylinders. The first of two chapters dedicated to the general variable mass system presents an approach to derive its equation of attitude motion. This discussion is followed by a mathematical proof of directional conservation of the variable mass system's angular momentum vector in the absence of external moments. This result is utilized, in the subsequent chapter, to visually interpretthe rotation of a torque-free, axisymmetric variable mass cylinder. The approach and results presented here strongly parallel the discussions on geometry of motion of axisymmetric rigid bodies found in classic texts on mechanics. The penultimate chapter, preceding the summary of the dissertation and direction for future work, presents an algorithm to estimatethe angular speeds of nearly axisymmetric variable mass cylinders. The variable mass cylinder idealization has historically been useful for gaining insight into the rotational behaviour of rockets.