Renal sympathetic denervation is currently performed in the treatment of resistant hypertension by interventionists who otherwise do not typically use radio-frequency (RF) energy ablation in their clinical practice. Adequate RF lesion formation is dependent upon good electrode-tissue contact, power delivery, electrode-tissue interface temperature, target-tissue impedance and the size of the catheter’s active electrode. There is significant interplay between these variables and hence an appreciation of the biophysical determinants of RF lesion formation is required to provide effective and safe clinical care to our patients. In this review article, we summarize the biophysics of RF ablation and explain why and how complications of renal sympathetic denervation may occur and discuss methods to minimise them.