  The issues of quintessence and cosmic acceleration can be discussed in the
framework of higher order curvature and torsion theories of gravity. We can
define effective pressure and energy density directly connected to the
curvature or to the torsion fields and then ask for the conditions to get an
accelerated expansion. Exact accelerated expanding solutions can be achieved
for several fourth order curvature or torsion theories so that we obtain an
alternative scheme to the standard quintessence scalar field, minimally coupled
to gravity, usually adopted. We discuss also conformal transformations in order
to see the links of quintessence between the Jordan and Einstein frames.
Furthermore, we take into account a torsion fluid whose effects become relevant
at large scale. Specifically, we investigate a model where a totally
antisymmetric torsion field is taken into account discussing the conditions to
obtain quintessence. We obtain exact solutions also in this case where dust
dominated Friedmann behavior is recovered as soon as torsion effects are not
relevant.
