Within the European Union there are annually about 1 300 000 accidents with physical injuries. Estimates indicate that accident costs add up to €160 billion, corresponding to 2 percent of the Union's GDP. On Sweden's roads alone 400-500 people are killed annualy and thousands are injured. Traffic accidents are, like in most other countries, one of the country's national health problems. Substantial resources are allocated to reduce the number of accidents and their consequences, once an accident occurs. The insurance industry is one part in this. The focus of this report is how insurance companies design their insurance premiums and the possibility to change this design in order to curb accident risks. Our starting point is that modern techniques makes it feasible to link the way in which the premium is calculated to actual behaviour. The fast development of in-vehicle "black box" technology provides prerequisits for observing driver behaviour and in particular speed relative to speed limits. By making speeders pay more than drivers that adhere to speed limits, the insurance system may affect average speed on the road network and consequently also the number and consequences of accidents. The report is made up of three parts. The first presents a review of international experiences of "Pay-as-You-Drive" and "Pay-as-You-Speed" applications. The second reviews technical aspects and the options available when selecting an appropriate solution. A third paper presents a blueprint for the way in which an insurance premium based on "Pay-as-You-Speed" could be designed in order to capture important incentive aspects of the system. It is suggested that the insurance industry should go ahead with the development of these techniques. It is, however, also acknowledged that the incentives of the industry may be insuffient to carry the implementation costs. Since society at large carries much more of the accident costs than the industry itself, this provides prima facie motive for government intervention in order to avoid a market failure. It is argued that the costs for establishing an open technical platform in vehicles and to organise the collection of data may be small relative to the potential benefits of the system.