We present first Doppler images of HD 51066 from observations in 1994, 1995, 1996 and 1997, and find evidence for a vanishing polar spot in accordance with the system's long-term brightness increase. Several small spots with Delta T~500 K appear also at low latitudes. Our cross-correlation maps indicate a latitude-dependent phase-shift pattern between annual maps. New and continuous BVRI photometry from 1996 to 1998 is presented and suggest a photometric period of 16.053+/-0.004 days, that we interpret to be the stellar rotation period. Additional optical spectroscopy and the Hipparcos data are used to obtain absolute stellar parameters for HD 51066. A comparison with evolutionary tracks and the assumption of angular-momentum and magnetic-flux conservation suggest that the main-sequence progenitor was a very rapidly-rotating Bp star with a several kiloGauß\ magnetic field. We also examine the Halpha line profiles in this star and find some evidence that its equivalent width is modulated with the stellar rotation period in phase with the photospheric starspots. Our radial velocities indicate that HD 51066 is likely a long-period (~10 yrs) spectroscopic binary and a preliminary orbit is presented. We emphasize that HD 51066 is an interesting target for studies of evolutionary angular-momentum loss because it is effectively single, significantly evolved but still rapidly rotating.