We develop a microscopic theory for the spin Seebeck effect (SSE) in Néel and canted phases of antiferromagnetic insulators. We calculate the DC spin current tunneling from the antiferromagnet to an attached metal, incorporating the spin-wave theory and the non-equilibrium Green's function approach. Our result shows a sign change of the spin current at the spin-flop phase transition between Néel and canted phases, which is in agreement with a recent experiment for the SSE of $\rm Cr_2O_3$ in a semi-quantitative level. The sign change can be interpreted from the argument based on the density of states of up- and down-spin magnons, which is related to the polarized-neutron scattering spectra. The theory also demonstrates that the spin current in the Néel phase is governed by the magnon correlation, while that in the canted phase consists of two parts: Contributions from not only the magnon dynamics but also the static transverse magnetization. This result leads to a prediction that at sufficiently low temperatures, the spin current non-monotonically changes as a function of magnetic field in the canted phase. Towards a more unified understanding of the SSE in antiferromagnets, we further discuss some missing links of theories of SSE: Interface properties, effects of the transverse spin moment in the canted phase, the spin-orbit coupling in the metal, etc. Finally, we compare the SSE of antiferromagnets with those of different magnetic phases such as ferromagnets, ferrimagnets, an one-dimensional spin liquid, a spin-nematic liquid, and a spin-Peierls (dimerized) phase.

25 pages, 14 figures, Open access