Open quantum dots provide a natural system in which to study both classical and quantum features of transport. From the classical point of view these dots possess a mixed phase space which yields families of closed, regular orbits as well as an expansive sea of chaos. An important question concerns the manner in which these classical states evolve into the set of quantum states that populate the dot in the quantum limit. In the reverse direction, the manner in which the quantum states evolve to the classical world is governed strongly by Zurek's decoherence theory. This was discussed from the quantum perspective in an earlier review (Ferry et al 2011 Semicond. Sci. Technol. 26 043001). Here, we discuss the nature of the various classical states, how they are formed, how they progress to the quantum world, and the signatures that they create in magnetotransport and general conductance studies of these dots.