Registration of range sensor measurements is an important task in mobile robotics and has received a lot of attention. Several iterative optimization schemes have been proposed in order to align three-dimensional (3D) point scans. With the more widespread use of high-frame-rate 3D sensors and increasingly more challenging application scenarios for mobile robots, there is a need for fast and accurate registration methods that current state-of-the-art algorithms cannot always meet. This work proposes a novel algorithm that achieves accurate point cloud registration an order of a magnitude faster than the current state of the art. The speedup is achieved through the use of a compact spatial representation: the Three-Dimensional Normal Distributions Transform (3D-NDT). In addition, a fast, global-descriptor based on the 3D-NDT is defined and used to achieve reliable initial poses for the iterative algorithm. Finally, a closed-form expression for the covariance of the proposed method is also derived. The proposed algorithms are evaluated on two standard point cloud data sets, resulting in stable performance on a par with or better than the state of the art. The implementation is available as an open-source package for the Robot Operating system (ROS).