A Simultaneous Localization and Mapping (SLAM) system must be robust to support long-term mobile vehicle and robot applications. However, camera and LiDAR based SLAM systems can be fragile when facing challenging illumination or weather conditions which degrade their imagery and point cloud data. Radar, whose operating electromagnetic spectrum is less affected by environmental changes, is promising although its distinct sensing geometry and noise characteristics bring open challenges when being exploited for SLAM. % However, there are still open challenges since most existing visual and LiDAR SLAM systems do not operate in bad weathers. This paper studies the use of a Frequency Modulated Continuous Wave radar for SLAM in large-scale outdoor environments. We propose a full radar SLAM system, including a novel radar motion tracking algorithm that leverages radar geometry for reliable feature tracking. It also optimally compensates motion distortion and estimates pose by joint optimization. Its loop closure component is designed to be simple yet efficient for radar imagery by capturing and exploiting structural information of the surrounding environment. % while a scheme to reject ambiguous loop closure candidates is also designed specifically for radar. Extensive experiments on three public radar datasets, ranging from city streets and residential areas to countryside and highways, show competitive accuracy and reliability performance of the proposed radar SLAM system compared to the state-of-the-art LiDAR, vision and radar methods. The results show that our system is technically viable in achieving reliable SLAM in extreme weather conditions, e.g. heavy snow and dense fog, demonstrating the promising potential of using radar for all-weather localization and mapping.