The Balloon Borne Experiment with a Superconducting Spectrometer (BESS) has measured the energy spectrum of cosmic-ray antiprotons between 0.18 and 4.20 GeV in eight flights between 1993 and 2002. Above about I GeV, models in which antiprotons are secondary products of the interactions of primary cosmic rays with the interstellar gas agree with the BESS antiproton spectrum. Below I GeV, the data show a possible excess antiproton flux compared to secondary model predictions, suggesting the presence of an additional source of antiprotons. The antiproton/proton ratios measured between 1993 and 1999, during the Sun's positive-polarity phase, are consistent with simple models of solar modulation. However, results from the 2000 flight, following the solar magnetic field reversal, show a sudden increase in the antiproton/proton ratio and tend to favor a charge-sign-dependent drift model. To extend BESS measurements to lower energies, an evolutionary instrument, BESS-Polar, is under construction for polar flight in 2004. Published by Elsevier Ltd on behalf of COSPAR.