We introduce 3D Moments, a new computational photography effect. As input we take a pair of near-duplicate photos, i.e., photos of moving subjects from similar viewpoints, common in people's photo collections. As output, we produce a video that smoothly interpolates the scene motion from the first photo to the second, while also producing camera motion with parallax that gives a heightened sense of 3D. To achieve this effect, we represent the scene as a pair of feature-based layered depth images augmented with scene flow. This representation enables motion interpolation along with independent control of the camera viewpoint. Our system produces photo-realistic space-time videos with motion parallax and scene dynamics, while plausibly recovering regions occluded in the original views. We conduct extensive experiments demonstrating superior performance over baselines on public datasets and in-the-wild photos.