  Doppler Imaging produces 2D global maps of rotating objects using
high-dispersion spectroscopy. When applied to brown dwarfs and extrasolar
planets, this technique can constrain global atmospheric dynamics and/or
magnetic effects on these objects in un- precedented detail. I present the
first quantitative assessment of the prospects for Doppler Imaging of
substellar objects with current facilities and with future giant ground-based
telescopes. Observations will have the greatest sensitivity in K band, but the
H and L bands will also be useful for these purposes. To assess the number and
availability of targets, I also present a compilation of all measurements of
photometric variability, rotation period (P), and projected rotational velocity
(v sin i) for brown dwarfs and exoplanets. Several bright objects are already
accessible to Doppler Imaging with currently available instruments. With the
development of giant ground-based telescopes, Doppler Imaging will become
feasible for many dozens of brown dwarfs and for the few brightest directly
imaged extrasolar planets (such as beta Pic b). The present set of measurements
of P, v sin i, and variability are incomplete for many objects, and the sample
is strongly biased toward early-type objects (< L5). Thus, surveys to measure
these quantities for later-type objects will be especially helpful in expanding
the sample of candidates for global weather monitoring via Doppler Imaging.
