  Nearly all proposed tests for the nature of dark energy measure some
combination of four fundamental observables: the Hubble parameter H(z), the
distance-redshift relation d(z), the age-redshift relation t(z), or the linear
growth factor D_1(z). I discuss the sensitivity of these observables to the
value and redshift history of the equation of state parameter w, emphasizing
where these different observables are and are not complementary. Demonstrating
time-variability of w is difficult in most cases because dark energy is
dynamically insignificant at high redshift. Time-variability in which dark
energy tracks the matter density at high redshift and changes to a cosmological
constant at low redshift is {\it relatively} easy to detect. However, even a
sharp transition of this sort at z_c=1 produces only percent-level differences
in d(z) or D_1(z) over the redshift range 0.4 < z < 1.8$, relative to the
closest constant-w model. Estimates of D_1(z) or H(z) at higher redshift,
potentially achievable with the Ly-alpha forest, galaxy redshift surveys, and
the CMB power spectrum, can add substantial leverage on such models, given
precise distance constraints at z < 2. The most promising routes to obtaining
sub-percent precision on dark energy observables are space-based studies of
Type Ia supernovae, which measure d(z) directly, and of weak gravitational
lensing, which is sensitive to d(z), D_1(z), and H(z).
