This paper reviews our attempts to understand the transport of magnetic flux on the Sun from the Babcock and Leighton models to the recent revisions that are being used to simulate the field over many sunspot cycles. In these models, the flux originates in sunspot groups and spreads outward on the surface via supergranular diffusion; the expanding patterns become sheared by differential rotation, and the remnants are carried poleward by meridional flow. The net result of all of the flux eruptions during a sunspot cycle is to replace the initial polar fields with new fields of opposite polarity. A central issue in this process is the role of meridional flow, whose relatively low speed is near the limit of detection with Doppler techniques. A compelling feature of Leighton’s original model was that it reversed the polar fields without the need for meridional flow. Now, we think that meridional flow is central to the reversal and to the dynamo itself.