The 1st International Equitation Science Symposium (ESS 2005) was designed to focus on the application of learning theory to horse training with the aim of improving the welfare of horses in the human domain. The organisers were a group of equine scientists, veterinarians, ethologists and behaviour therapists who share the view that human-related causes of undesirable equine behaviours can be largely attributed to the current lack of science in equitation. Humans influence the behaviour of horses, in-hand and under saddle, with stimuli from their hands on the reins and their legs on the sides of the horse and more discreetly with the use of their seat, weight position and movement. Furthermore, devices such as whips and spurs are also used by some. Horse riding at its most humane relies on subtle interactions between horses and humans. This occurs through the correct application of negative reinforcement and the subsequent transfer of stimulus control to various classically conditioned cues (such as those coming from the seat). It is surprising therefore, that so little scientific endeavour has been directed towards the effects of aversive stimuli on horses and the ways in which horses respond to stimuli of human origin. The performance of the horse under saddle and the consequent development of riding instruction tend to focus on outcomes rather than mechanisms. Additionally, riding manuals have historically by-passed the central tenets of learning theory. Since the ideals of equestrian technique combine art and science, students of equitation encounter a few measurable variables such as tempo, rhythm and outline alongside many more conceptual ones such as harmony, looseness, respect and leadership. This unbalanced mixture and the shortage of mechanistic substance frustrate attempts to express equestrian technique in empirical terms and account for some of the confusion and conflict that arises in many human-horse dyads. Among the specific areas explored in the proceedings are an analysis of different approaches currently used for achieving key outcomes in dressage horses. The impact of training and management on the welfare of horses is also considered along with the role of behaviour-related disorders as a cause of industry wastage. Other topics include the way in which horses of different breeds may see the world differently and the effect of negatively reinforced head-lowering on horses. It is worth noting that there is evidence of confusion about terminology among horse people. This presumably compounds a lack of rigour in identifying problem behaviours in horses. The editors of the proceedings have contributed a paper that discusses the need for objective definitions in equitation science and offers some useful starting points