  We study the observational constraints of CMB temperature and polarization
anisotropies on models of dark energy, with special focus on models with
variation in properties of dark energy with time. We demonstrate that the key
constraint from CMB observations arises from the location of acoustic peaks. An
additional constraint arises from the limits on Omega_nr from the relative
amplitudes of acoustic peaks. Further, we show that the distance to the last
scattering surface is not how the CMB observations constrain the combination of
parameters for models of dark energy. We also use constraints from Supernova
observations and show that unlike the Gold and Silver samples, the SNLS sample
prefers a region of parameter space that has a significant overlap with the
region preferred by the CMB observations. This is a verification of a
conjecture made by us in an earlier work. We discuss combined constraints from
WMAP5 and SNLS observations. We find that models with w ~ -1 are preferred for
models with a constant equation of state parameters. In case of models with a
time varying dark energy, we show that constraints on evolution of dark energy
density are almost independent of the type of variation assumed for the
equation of state parameter. This makes it easy to get approximate constraints
from CMB observations on arbitrary models of dark energy. Constraints on models
with a time varying dark energy are predominantly due to CMB observations, with
Supernova constraints playing only a marginal role.
