  We review millimeter interferometric phase variations caused by variations in
the precipitable water vapor content of the troposphere, and we discuss
techniques proposed to correct for these variations. We present observations
with the Very Large Array at 22 GHz and 43 GHz designed to test these
techniques. We find that both the Fast Switching and Paired Array calibration
techniques are effective at reducing tropospheric phase noise for radio
interferometers. In both cases, the residual rms phase fluctuations after
correction are independent of baseline length for b > b_{eff}. These techniques
allow for diffraction limited imaging of faint sources on arbitrarily long
baselines at mm wavelengths. We consider the technique of tropospheric phase
correction using a measurement of the precipitable water vapor content of the
troposphere via a radiometric measurement of the brightness temperature of the
atmosphere. Required sensitivities range from 20 mK at 90 GHz to 1 K at 185 GHz
for the MMA, and 120 mK for the VLA at 22 GHz. The minimum gain stability
requirement is 200 at 185 GHz at the MMA assuming that the astronomical
receivers are used for radiometry. This increases to 2000 for an uncooled
system. The stability requirement is 450 for the cooled system at the VLA at 22
GHz. To perform absolute radiometric phase corrections also requires knowledge
of the tropospheric parameters and models to an accuracy of a few percent. It
may be possible to perform an `empirically calibrated' radiometric phase
correction, in which the relationship between fluctuations in brightness
temperature differences with fluctuations in interferometric phases is
calibrated by observing a celestial calibrator at regular intervals.
