Authors:Wargelin et alAbstract:Stars of stellar type later than about M3.5 are believed to be fully convective and therefore unable to support magnetic dynamos like the one that produces the 11-year solar cycle. Because of their intrinsic faintness, very few late M stars have undergone long-term monitoring to test this prediction, which is critical to our understanding of magnetic field generation in such stars. Magnetic activity is also of interest as the driver of UV and X ray radiation, as well as energetic particles and stellar winds, that affect the atmospheres of close-in planets that lie within habitable zones, such as the recently discovered Proxima b. We report here on several years of optical, UV, and X-ray observations of Proxima Centauri (GJ 551; dM5.5e): 15 years of ASAS photometry in the V band (1085 nights) and 3 years in the I band (196 nights), 4 years of Swift XRT and UVOT observations (more than 120 exposures), and 9 sets of X-ray observations from other X-ray missions (ASCA, XMM-Newton, and three Chandra instruments) spanning 22 years. We confirm previous reports of an 83-day rotational period and find strong evidence for a 7-year stellar cycle, along with indications of differential rotation at about the solar level. X-ray/UV intensity is anti-correlated with optical V-band brightness for both rotational and cyclical variations. From comparison with other stars observed to have X-ray cycles we deduce a simple empirical relationship between X-ray cyclic modulation and Rossby number, and we also present Swift UV grism spectra covering 2300–6000 Å.