Bridge weigh-in-motion (B-WIM) is a method by which the axle weights of a vehicle travelling at full highway speed can be determined using a bridge instrumented with sensors. Since the sensors are attached to the underside of a bridge, the instrumentation can be installed without disruption to traffic. This paper looks at the history of B-WIM, beginning with early work on weigh-in-motion technologies in the 1960's leading to its invention by Fred Moses and George Goble in the United States in the mid 1970's. Particular attention is devoted to Moses' original algorithm, which has been used by many systems since 1979 and is still utilized today by commercial developers of B-WIM systems. Research initiatives in Australia and Europe over the past 15 years have focused on improving B-WIM accuracy either by improving Moses' original algorithm or by developing new methods. The moving force identification (MFI) method models the dynamic fluctuation of axle forces on the bridge and holds particular promise. B-WIM accuracy depends on bridge site conditions as well as the particular data processing algorithm. The accuracy classifications of several B-WIM installations reported in the literature are summarized in this paper. Current accuracy levels are sufficient for selecting vehicles to be weighed using static scales, but insufficient for direct enforcement.