With the availability of spectrally pure lasers and the ability to precisely measure optical frequencies, it appears the era of optical atomic clocks has begun. At the expense of signal-to-noise ratio, in one project at NIST we have used single trapped atomic ions because uncertainties in systematic effects are smallest, reaching Df/f0 = 0.8 x 10-17. At this level, many effects, including those due to special and general relativity, must be calibrated and corrected for.