The high-z type Ia supernova magnitude-redshift relation, large-scale
structure of galaxies, and the cosmic microwave background observations
suggest that the expansion rate of our universe is currently under
acceleration. Especially, our cosmological framework demands the presence
of substantial amount of dark energy with repulsive nature like the
cosmological constant. In this talk I briefly review several dark energy
models that have been proposed so far and summarize the current status
of dark energy model constraints with astronomical observations, together
with my recent research works on this issue.