A survey of variations in the radial-velocity and visual brightness of the star Betelgeuse (alpha-Orionis) over the last six decades is presented. On the basis of a comparison of the results of several observations, it is suggested that major disturbances in Betelgeuse's atmosphere are likely to occur in the year or two following the minimum in the six-year velocity curve. A coordinated observing program is proposed to take place during and after the next minimum, which is predicted to take place in early 1984. The desirable observations include multicolor photometry (particularly in the infrared), polarization measurements, and spectroscopy.