Catheter-based renal denervation (RDN) leads to a considerable decrease of blood pressure in the vast majority of patients with resistant hypertension. However, only minor or no blood pressure change is achieved in some patients. This non-reponse is defined as a reduction of office systolic blood pressure of less than 10 mmHg following RDN. The rates of non-response vary between 8-37%. Here several causes are discussed such as inappropriate patient selection, an ineffective procedure, the subordinate contribution of sympathetic activation for the maintenance of hypertension, and patient conditions such as non-adherence to drug therapy. Based on current evidence, an ideal candidate for RDN has high baseline blood pressure, which is known to be the best predictor for blood pressure reduction after RDN. In order to ensure treatment success further criteria have to be fulfilled, such as exclusion of secondary hypertension and optimised medical therapy.