Abstract : Antideuterons are among the most promising galactic cosmic ray-related targets for dark matter indirect detection. Currently only upper limits exist on the flux, but the development of new experiments, such as GAPS and AMS-02, provides exciting perspectives for a positive measurement in the near future. In this Paper, we present a novel and updated calculation of both the secondary and primary antideuteron fluxes. We employ a two-zone diffusion model which successfully reproduces cosmic-ray nuclear data and the observed antiproton flux. We review the nuclear and astrophysical uncertainties and provide an up to date secondary (i.e. background) antideuteron flux. The primary (i.e. signal) contribution is calculated for generic WIMPs annihilating in the galactic halo: we explicitly consider and quantify the various sources of uncertainty in the theoretical evaluations. Propagation uncertainties, as is the case of antiprotons, are sizeable. Nevertheless, antideuterons offer an exciting target for indirect dark matter detection for low and intermediate mass WIMP dark matter. We then show the reaching capabilities of the future experiments for neutralino dark matter in a variety of supersymmetric models.