  The reason for the present accelerated expansion of the Universe stands as
one of the most profound questions in the realm of science, with deep
connections to both cosmology and fundamental physics. From a cosmological
point of view, physical models aimed at elucidating the observed expansion can
be categorized into two major classes: dark energy and modified gravity. We
review various major approaches that employ a single scalar field to account
for the accelerating phase of our present Universe. Dynamical system analysis
is employed in several important models to seek for cosmological solutions that
exhibit an accelerating phase as an attractor. For scalar field models of dark
energy, we consistently focus on addressing challenges related to the
fine-tuning and coincidence problems in cosmology, as well as exploring
potential solutions to them. For scalar-tensor theories and their
generalizations, we emphasize the importance of constraints on theoretical
parameters to ensure overall consistency with experimental tests. Models or
theories that could potentially explain the Hubble tension are also emphasized
throughout this review.
