  We characterize the variation in photometric response of the Dark Energy
Camera (DECam) across its 520~Mpix science array during 4 years of operation.
These variations are measured using high signal-to-noise aperture photometry of
$>10^7$ stellar images in thousands of exposures of a few selected fields, with
the telescope dithered to move the sources around the array. A calibration
procedure based on these results brings the RMS variation in aperture
magnitudes of bright stars on cloudless nights down to 2--3 mmag, with <1 mmag
of correlated photometric errors for stars separated by $\ge20$". On cloudless
nights, any departures of the exposure zeropoints from a secant airmass law
exceeding >1 mmag are plausibly attributable to spatial/temporal variations in
aperture corrections. These variations can be inferred and corrected by
measuring the fraction of stellar light in an annulus between 6" and 8"
diameter. Key elements of this calibration include: correction of amplifier
nonlinearities; distinguishing pixel-area variations and stray light from
quantum-efficiency variations in the flat fields; field-dependent color
corrections; and the use of an aperture-correction proxy. The DECam response
pattern across the 2-degree field drifts over months by up to $\pm7$ mmag, in a
nearly-wavelength-independent low-order pattern. We find no fundamental
barriers to pushing global photometric calibrations toward mmag accuracy.
