Weak lensing surveys conducted at radio wavelengths offer unique and powerful features which can enhance measurements made with typical optical/near-infrared telescopes. However, since appropriate radio surveys are still in their infancy, development of radio data analysis techniques is required. This involves using pathfinding surveys to understand radio source populations, as well as developing methods to reliably extract galaxy shapes. This thesis presents early advances in radio weak lensing using state of the art surveys, and the results obtained will inform survey strategies and data analysis pipelines of future surveys such as those of the SKA.