In 1957, Landauer revolutionized the approach to the treatment of transport in condensed matter systems through the concept that the conductance could be directly related to the transmission coefficient through the system. Recently, this idea has become all pervasive in the study of mesoscopic systems, Here, we discuss the transport of ballistic carriers through strongly confined (but open) systems, known as quantum dots. The idea of transmission allows the connection of both classical and quantum concepts, and this opens the door to extend these studies to that of the quantum-to-classical transition. (C) 1998 Academic Press Limited.