Telematics data provide real-time information that can be used to develop new insurance pricing models in all lines, ranging from motor insurance to homeowners and health insurance. We focus specifically on motor insurance, where telematics data capture information on such variables as driver speed, acceleration, braking, and cornering. The preprocessing of telematics data and their synchronization with claims records are discussed, and classical econometric models for the estimation of claims frequency models that incorporate the features of telematics are presented. Machine learning algorithms can identify patterns in telematics data that are not otherwise immediately apparent, boost classical models, and serve to create risk scores. Econometrics modeling and machine learning of telematics insurance data facilitates dynamic policy pricing based on usage, and more personalized premiums reflecting individual driving behavior, which in turn can incentivize safer driving. Recent advances, including the use of contextual data on weather, traffic congestion, and road state, are briefly described. Regulatory constraints, contract choice, ethical issues, and practical insights regarding the adoption of telematics technology in motor insurance are presented.