The Thunderstorm Observation by Radar (ThOR) algorithm is an objective and tunable Lagrangian approach to cataloging thunderstorms. ThOR uses observations from multiple sensors (principally multisite surveillance radar data and cloud-to-ground lightning) along with established techniques for fusing multisite radar data and identifying spatially coherent regions of radar reflectivity (clusters) that are subsequently tracked using a new tracking scheme. The main innovation of the tracking algorithm is that, by operating offline, the full data record is available, not just previous cluster positions, so all possible combinations of object sequences can be developed using all observed object positions. In contrast to Eulerian methods reliant on thunder reports, ThOR is capable of cataloging nearly every thunderstorm that occurs over regional-scale and continental United States (CONUS)-scale domains, thereby enabling analysis of internal properties and trends of thunderstorms. ThOR is verified against 166 manually analyzed cluster tracks and is also verified using descriptive statistics applied to a large (~35 000 tracks) sample. Verification also relied on a benchmark tracking algorithm that provides context for the verification statistics. ThOR tracks are shown to match the manual tracks slightly better than the benchmark tracks. Moreover, the descriptive statistics of the ThOR tracks are nearly identical to those of the manual tracks, suggesting good agreement. When the descriptive statistics were applied to the ~35 000-track dataset, ThOR tracking produces longer (statistically significant), straighter, and more coherent tracks than those of the benchmark algorithm. Qualitative assessment of ThOR performance is enabled through application to a multiday thunderstorm event and comparison to the behavior of the Storm Cell Identification and Tracking (SCIT) algorithm