The main AB pair of the nearby Alpha Centauri triple system has one of the most extensive X-ray records of any cosmic object, stretching over three decades (following the initial discovery as an unresolved source by HEAO-1). The primary, Alpha Cen A (G2V), is a near twin of the Sun, with a similarly soft (1-2 MK) corona. The secondary, Alpha Cen B (K1V), is more active than the Sun, with a generally harder coronal spectrum. Here, recent spatially resolved measurements of the pair (8" apart in 2009, decreasing to a minimum of 4" circa 2016) by Chandra's High Resolution Camera are compared, on a common basis, with previous pointings from ROSAT and XMM-Newton, extending back more than a decade. The combined time series suggests that Alpha Cen B was near X-ray maximum in the mid-1990's, minimum in the late-1990's, then peaked again in 2004-2005. In the more recent Chandra segment, B was declining in 2006 and 2007, bottomed out in 2008, and as of May 2009 appears to be rising again. The roughly 8-year X-ray modulation is shorter than the solar 11-year sunspot period, although the cycle depth is similar (factor of 5 in 0.2-2 keV band). Meanwhile, Alpha Cen A showed minimal variability 1995-2000, a decline between 2003 and 2005, and like the secondary presently is mired in an activity lull, depressed a factor of 2 or so from the mid-1990's level. (In fact, as seen by XMM-Newton, the primary "fainted" from view in early 2005. Although the disappearance--representing a factor of 50 decline in the apparent count rate--was stunning at the time, it now is recognized as an artifact of the poor low-energy response of thick-filtered MOS1 and pn.) The Chandra study, which included a remarkable "smoking gun" LETGS spectrum in mid-2007, has emphasized that much of the high energy radiative output of cool-corona objects like the Sun falls at longer wavelengths than are recorded efficiently by contemporary stellar instruments, rendering the coronal luminosity and cycle depth strongly dependent on the energy span of the measurements. This has a broad-reaching impact on assessing coronal heating requirements, and the variations over long term activity cycles.