Recently, observations of spiral and S0 galaxies have shown that some disk galaxies have counterrotating disks which are cospatial with the primary disk, but rotating in the opposite sense. The most straightforward explanation for these puzzling systems is that they result from the accretion of gas by the primary disk. If the accreted gas has a net angular momentum in the opposite sense to the primary disk's rotation, then a counterrotating disk can form. I will present the results of numerical simulations (combining gravity and gas dynamics), demonstrating that massive counterrotating disks can form in less than a Hubble time either by continuous infall of intergalactic gas or by the cannibalization of a very gas-rich dwarf. For illustrative purposes, I will focus on the curious case of NGC 4138, a spiral galaxy in which a counterrotating disk appears to be currently forming.