Traditional edgewise orthodontic mechanics are significantly limited in their ability to provide incisor torque control because of the limitations of bracket-to-bracket mechanics and the poorly defined reciprocal actions inherently produced. Attempts to address this issue clinically have been largely empirical. The science of mechanics dictates that all incisor torque control mechanisms must act through one of two basic principles: the moment of a couple or the moment of a force. The torquing arch is a modification of the traditional edgewise system and employs the moment of a couple to achieve incisor torque control and precise definition of reciprocal effects. The torquing arch force system includes a large moment to rotate incisors in a crown facial/root lingual direction, and concurrent equilibrium forces to extrude incisors and intrude molars. Alternatively, the base arch uses the moment of a force to also rotate incisors in a crown facial/root lingual direction. The base arch, however, includes a large moment to rotate molars in a crown distal/root mesial direction, and concurrent equilibrium forces to intrude incisors and extrude molars. Depending on how they are employed, torquing arches and base arches may also rotate molars in a faciolingual direction, enhance or diminish posterior anchorage, and increase or conserve arch perimenter. Contemporary quality orthodontic care requires an awareness and control of all of the forces created by orthodontic appliances.