  We extend recent work on the relation of 4d and 3d IR dualities of
supersymmetric gauge theories with four supercharges to the case of orthogonal
gauge groups. The distinction between different SO(N) gauge theories in 4d
plays an important role in this relation. We show that the 4d duality leads to
a 3d duality between an SO(N_c) gauge theory with N_f flavors and an
SO(N_f-N_c+2) theory with N_f flavors and extra singlets, and we derive its
generalization in the presence of Chern-Simons terms. There are two different
O(N) theories in 3d, which we denote by O(N)_\pm, and we also show that the
O(N_c)_- gauge theory is dual to a Spin(N_f-N_c+2) theory, and derive from 4d
the known duality between O(N_c)_+ and O(N_f-N_c+2)_+. We verify the
consistency of these 3d dualities by various methods, including index
computations.
