  Quintessence is a canonical scalar field introduced to explain the late-time
cosmic acceleration. The cosmological dynamics of quintessence is reviewed,
paying particular attention to the evolution of the dark energy equation of
state w. For the field potentials having tracking and thawing properties, the
evolution of w can be known analytically in terms of a few model parameters.
Using the analytic expression of w, we constrain quintessence models from the
observations of supernovae type Ia, cosmic microwave background, and baryon
acoustic oscillations. The tracking freezing models are hardly distinguishable
from the LCDM model, whereas in thawing models the today's field equation of
state is constrained to be w_0<-0.7 (95 % CL). We also derive an analytic
formula for the growth rate of matter density perturbations in dynamical dark
energy models, which allows a possibility to put further bounds on w from the
measurement of redshift-space distortions in the galaxy power spectrum. Finally
we review particle physics models of quintessence- such as those motivated by
supersymmetric theories. The field potentials of thawing models based on a
pseudo-Nambu-Goldstone boson or on extended supergravity theories have a nice
property that a tiny mass of quintessence can be protected against radiative
corrections.
