  We study the power of upcoming weak lensing surveys to probe dark energy.
Dark energy modifies the distance-redshift relation as well as the matter power
spectrum, both of which affect the weak lensing convergence power spectrum.
Some dark-energy models predict additional clustering on very large scales, but
this probably cannot be detected by weak lensing alone due to cosmic variance.
With reasonable prior information on other cosmological parameters, we find
that a survey covering 1000 sq. deg. down to a limiting magnitude of R=27 can
impose constraints comparable to those expected from upcoming type Ia supernova
and number-count surveys. This result, however, is contingent on the control of
both observational and theoretical systematics. Concentrating on the latter, we
find that the {\it nonlinear} power spectrum of matter perturbations and the
redshift distribution of source galaxies both need to be determined accurately
in order for weak lensing to achieve its full potential. Finally, we discuss
the sensitivity of the three-point statistics to dark energy.
