  Bringmann and Lovejoy introduced a rank for overpartition pairs and
investigated its role in congruence properties of $\bar{pp}(n)$, the number of
overpartition pairs of n. In particular, they applied the theory of Klein forms
to show that there exist many Ramanujan-type congruences for the number
$\bar{pp}(n)$. In this paper, we shall derive two Ramanujan-type identities and
some explicit congruences for $\bar{pp}(n)$. Moreover, we find three ranks as
combinatorial interpretations of the fact that $\bar{pp}(n)$ is divisible by
three for any n. We also construct infinite families of congruences for
$\bar{pp}(n)$ modulo 3, 5, and 9.
