A peregrine falcon will reach speeds of 200 miles per hour as it hurtles towards its prey – a pigeon that is itself in full flight as it attempts to escape the looming predator. Despite the speeds involved, the peregrine will still successfully adjust its position to elegantly and precisely intercept its prey. Ants who have successfully navigated the long distance between their foraging spot and their nest dozens of times will drastically overshoot their destination if the size of their legs are doubled by the addition of stilts. These are just two examples of the crucial relationship between the speed of movement and successful navigation strategies. They necessitate that animals keep track of their movement speed and use it to precisely and instantly modify where they think they are and where they want to go. Here we review the heavily interconnected neural circuitry that has evolved to integrate speed and space in the brain. We start with the rate and temporal codes for speed in the hippocampus and work backwards towards both the motor and sensory systems. As we trace the flow of the speed signal across these circuits, we highlight the need to design experiments that systematically attempt to differentiate the respective contributions of motor efference copy and sensory inputs. In particular, we emphasize the importance of high-resolution, precise tracking of the latency of speed-encoding compared to the actual change in speed as a precise way to disentangle the sensory versus motor computations that enable successful spatial navigation at very different speeds.