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As animals that move in a 3D world and interact with 3D objects, it is very important for our survival that our visual systems provide two- and three-dimensional motion perception. Over 4 experimental chapters, we used psychophysical methods to consider several questions about how the human brain processes speed information in two and three dimensions. In Chapter 2, we investigated whether making three-dimensional motion more realistic than in many previous human vision studies, by adding accelerations on the retina to our stimuli, improved our ability to discriminate speed changes. We found that adding retinal acceleration to our stimuli did not offer performance enhancement. In Chapter 3, we wanted to understand whether monocular or binocular cues were more important for discriminating speed changes for motion in depth. Our results were inconclusive, but the apparent difficulty of the speed change discrimination task led us to compare performance in these tasks to that for speed discrimination: we found speed change discrimination to be more difficult. It is often possible to use distance or duration information for speed discrimination, but not for speed change discrimination, so we also investigated whether participants use speed information for speed discrimination. Participants used a range of cues, and may have changed the cue they used from trial to trial. In Chapter 4, we investigated with novel experimental designs whether participants used speed, distance, duration or a combination of cues to make speed and speed change discrimination judgements. We found participants used speed information alone for both tasks. Finally, in Chapter 5 we considered whether speed change discrimination was difficult because speed information was combined over space or time. Neither combination of speed information across time, or across space, was responsible speed change discrimination difficulty. Overall, our findings contribute to our understanding of speed perception for moving objects.