For centuries, a goal of training in many equestrian disciplines has been to straighten the horse, which is considered a key element in achieving its responsiveness and suppleness. However, laterality is a naturally occurring phenomenon in horses and encompasses body asymmetry, motor laterality and sensory laterality. Furthermore, forcibly counterbalancing motor laterality has been considered a cause of psychological imbalance in humans. Perhaps asymmetry and laterality should rather be accepted, with a focus on training psychological and physical balance, coordination and equal strength on both sides instead of enforcing “straightness”. To explore this, we conducted a review of the literature on the function and causes of motor and sensory laterality in horses, especially in horses when trained on the ground or under a rider. The literature reveals that body asymmetry is innate but does not prevent the horse from performing at a high level under a rider. Motor laterality is equally distributed in feral horses, while in domestic horses, age, breed, training and carrying a rider may cause left leg preferences. Most horses initially observe novel persons and potentially threatening objects or situations with their left sensory organs. Pronounced preferences for the use of left sensory organs or limbs indicate that the horse is experiencing increased emotionality or stress, and long-term insufficiencies in welfare, housing or training may result in left shifts in motor and sensory laterality and pessimistic mentalities. Therefore, increasing laterality can be regarded as an indicator for insufficiencies in housing, handling and training. We propose that laterality be recognized as a welfare indicator and that straightening the horse should be achieved by conducting training focused on balance, coordination and equal strength on both sides.