On-road vehicle detection is essential for perceiving driving settings, and localizing the detected vehicle helps drivers predict possible risks and avoid collisions. However, there are limited works on vehicle detection with partial appearance, and the method for partially visible vehicle localization has not been explored. In this paper, a novel framework for vehicle detection and localization with partial appearance is proposed using stereo vision and geometry. First, the original images from the stereo camera are processed to form a v-disparity map. After object detection using v-disparity, vehicle candidates are generated with prior knowledge of possible vehicle locations on the image. Deep learning-based verification completes vehicle detection. For each detected vehicle, partially visible vehicle tracking algorithm is newly introduced. To track partially visible vehicles, this algorithm detects the vehicle edge on the ground, defined as the grounded edge, and then selects a reference point for Kalman filter tracking. Finally, a rectangular box is drawn on the bird's eye view to represent vehicle's longitudinal and lateral location. The proposed system successfully performs partially visible vehicle detection and tracking. For testing the localization performance, the datasets in a highway and an urban setting are used and provide less than 1.5 m longitudinal error and 0.4 m lateral error in standard deviation. (C) 2018 Elsevier B.V. All rights reserved.