The wake bifurcations behind two circular disks in tandem arrangement are investigated through numerical simulations. The separation distance between the disks, S/d, is chosen at 1, 2, 4, and 6, and the Reynolds number, Re, lies in the range of 100 <= Re <= 500. The wake dynamics are examined in terms of the flow structures as well as drag and lift coefficient characteristics. Seven main wake regimes are observed in the considered (Re,S/d) space: steady state (SS), Zig-zig (Zz) mode, standing wave mode, periodic state with reflectional symmetry breaking (RSB), periodic state with double-helical (DH) structures shedding, periodic state with double-hairpin-loop (DHL) shedding, and weakly chaotic state. Among these bifurcations, the DH and DHL wake modes are reported in the tandem disk wakes, which are not observed in a single disk wake. Compared with the single disk wake, the first bifurcation leading to the SS mode is always delayed in tandem configuration, which is especially evident for the case of S/d = 1. For the second bifurcation leading to an unsteady state, some differences lie in the wake mode for different tandem configurations. The second bifurcation leads to the Zz wake mode for the cases S/d = 1, 2, and 4, and the RSB mode for S/d = 6. In the scenario of S/d = 1, the bifurcations are similar to those of a thick disk, suggesting that a shorter separation distance in this configuration has equivalent effects as increasing the thickness in the case of a single disk. In the scenario of S/d = 2, the bifurcations are complex and quite different from those in a single disk wake, indicating that the interaction between two disks in tandem arrangement is stronger when the trailing disk is located close to the end of the recirculation region of the leading one. In the scenario of S/d = 6, the bifurcations resemble those of a single disk wake, except for an observed DHL wake mode. In addition, the variations of the vortex shedding frequency for the unsteady states are investigated and presented.