The relationship between spatial skills training and computer science learning is unclear. Reported experiments provide tantalising, though not convincing, evidence that training a programming student's spatial skills may accelerate the development of their programming skills. Given the well-documented challenge of learning to program, such acceleration would be welcomed. Despite the experimental results, no attempt has been made to develop a model of how a linkage between spatial skills and computer science ability might operate, hampering the development of a sound research programme to investigate the issue further. This paper surveys the literature on spatial skills and investigates the various underlying cognitive skills involved. It poses a theoretical model for the relationship between computer science ability and spatial skills, exploring ways in which the cognitive processes involved in each overlap, and hence may influence one another. An experiment shows that spatial skills typically increase as the level of academic achievement in computer science increases. Overall, this work provides a substantial foundation for, and encouragement to develop, a major research programme investigating precisely how spatial skills training influences computer science learning, and hence whether computer science education could be significantly improved.