Dark matter may be composed of superWIMPs, superweakly-interacting massive particles produced in the late decays of other particles. We focus here on the well-motivated supersymmetric example of gravitino LSPs. Gravitino superWIMPs share several virtues with the well-known case of neutralino dark matter: they are present in the same supersymmetric frameworks (supergravity with R-parity conservation) and naturally have the desired relic density. In contrast to neutralinos, however, gravitino superWIMPs are impossible to detect by conventional dark matter searches, may explain an existing discrepancy in Big Bang nucleosynthesis, predict observable distortions in the cosmic microwave background, and imply spectacular signals at future particle colliders.