The speed at which people elect to travel is affected by vehicle and road design; by limits to speed and enforcement of those limits; by traffic control, signs, and markings; and so forth. The speed at which people travel, in turn, affects road safety. In this context two questions arise: (a) How is the evolution of speed over time and space affected by what drivers do? (b) How does speed affect safety? This paper reviews what is known, notes the gaps in knowledge, and describes where opinions differ and why. Unfortunately, despite decades of speed measurement and monitoring, the evolution of speed over time is poorly documented, and the understanding of what drives the evolution is largely missing. It is known that speeds evolve over time, but not why; it is known that there is some spillover of the change from one road to another, but its size or extent cannot be predicted. This is a neglected field of inquiry. More is known in answer to Question b. There can be no reasonable doubt that if speed increases while other conditions (vehicles, roads, medical services) remain unchanged, the accidents that occur will tend to be more severe. However, the prevalent and strongly held belief that the greater the speed, the higher is the probability that accidents will occur is, at present, not well supported by research. Even so, given a change in mean speed, one can predict the consequences in injuries and fatalities and this paper discusses how to do so.