  We use the correspondence between the $f(R)$ theory and an Einstein-scalar
field system to study late-time dynamics of solutions of $f(R)$ theory. We
discuss how reasonable assumptions on the potential of the scalar field lead to
restrictions on the function $f(R)$ and use known results for the scalar field
system to gain results on solutions of the $f(R)$ theory. In particular, we
prove accelerated expansion at late times for several different categories of
functions $f(R)$ that satisfy certain restrictions.
