Situational awareness is crucial for autonomous driving in urban environments. This paper describes the moving vehicle detection and tracking module that we developed for our autonomous driving robot Junior. The robot won second place in the Urban Grand Challenge, an autonomous driving race organized by the U.S. Government in 2007. The module provides reliable detection and tracking of moving vehicles from a high-speed moving platform using laser range finders. Our approach models both dynamic and geometric properties of the tracked vehicles and estimates them using a single Bayes filter per vehicle. We present the notion of motion evidence, which allows us to overcome the low signal-to-noise ratio that arises during rapid detection of moving vehicles in noisy urban environments. Furthermore, we show how to build consistent and efficient 2D representations out of 3D range data and how to detect poorly visible black vehicles. Experimental validation includes the most challenging conditions presented at the Urban Grand Challenge as well as other urban settings.