Let X be a smooth projective variety over the complex numbers. One way to study X is to examine the `positive’ divisors that it admits; more precisely, one can consider the cones (in the Néron-Severi space of X) that are spanned by classes of ample or effective divisors. We will review the key features of the ample cone and use this as a guide to discuss the pseudoeffective cone, which is the closure of the cone of effective divisors. The goal is to describe the interior and the dual of the pseudoeffective cone in geometric terms.