  The cosmic acceleration is one of the most significant cosmological
discoveries over the last century. Following the more accurate data a more
dramatic result appears: the recent analysis of the observation data
(especially from SNe Ia) indicate that the time varying dark energy gives a
better fit than a cosmological constant, and in particular, the equation of
state parameter $w$ (defined as the ratio of pressure to energy density)
crosses -1 at some low redshift region. This crossing behavior is a serious
challenge to fundamental physics. In this article, we review a number of
approaches which try to explain this remarkable crossing behavior. First we
show the key observations which imply the crossing behavior. And then we
concentrate on the theoretical progresses on the dark energy models which can
realize the crossing -1 phenomenon. We discuss three kinds of dark energy
models: 1. two-field models (quintom-like), 2. interacting models (dark energy
interacts with dark matter), and 3. the models in frame of modified gravity
theory (concentrating on brane world).
