Cardiac resynchronization therapy (CRT) is an effective option for the management of heart failure (HF) patients with left ventricular systolic dysfunction and prolongation of the QRS interval. Unfortunately, a variable proportion of eligible patients fail to benefit from this treatment, the so-called "non-responders". Despite intensive investigations aimed at identifying reliable diagnostic tools, additional to standard criteria, for the selection of responders, partly due to the complexity and multi-factorial nature of the mechanism underlying response, no conclusive evidence is currently available about which of the many variables assessed may predict individual response and should be included in selection criteria. Accordingly, even if labeled as a non-responder, a patient should receive a CRT device being the certain risk of withholding the treatment more consistent than the potential risk of being a non-responder. However, a possible third profile of patients along with responders and non-responders is emerging consisting of a limited subset of individuals, mainly among those with HF of ischemic aetiology, who simply do not possess the anatomical requisite for conventional biventricular pacing to be effective. Such patients may be referred to as those who cannot respond to CRT and their identification is potentially feasible by integrating non-invasive imaging findings and of clinical relevance in the definition of the therapeutic strategy. In conclusion, this review will provide an analysis of gathered data about the selection of candidates to CRT beyond responders and non-responders with the perspective of the potential characterization of patients who cannot respond to CRT.