Craniopagus twins (CPT) are an uncommon, highly fascinating accident of nature. The clinical pathology of this complex entity is reviewed and placed in perspective. A logical classification aids understanding of the anomaly, and is essential to gauge outcome from separation attempts. ‘Partial forms’ lack significant shared dural venous sinuses (SDVS) and ‘Total forms’ with SDVS also exhibit more severe compressional brain distortion. Our classification consists of Partial Angular (PA), Partial Vertical (PV), Total Angular (TA) and Total Vertical (TV, formerly O'Connell Types I–III). Total vertical has a continuous cranium, and inter-twin axial facial rotation <40° (Type I), 140–180° (Type II) or intermediate (Type III). The term ‘Angular’ denotes an inter-twin longitudinal angle below 140°, regardless of axial rotation. Our review categorized 64 well-delineated CPT, including 41 operative separation attempts in small children since initial success in 1952. Just over one-half were TV, almost one-third TA, and partial forms accounted for the remaining one-sixth. About 30% of CPT had shared or fused brain tissue, and a similar percentage of TA twins shared a posterior fossa. Partial forms had significantly higher birth weights, were separated at an earlier age (6 versus 11 months) and had lower mortality and better outcome compared with Total forms. A multi-staged surgical separation for Total CPT had a significantly better mortality than single-staged separation. Discussion emphasizes embryological, anatomical and clinical aspects of the malformation, with emphasis upon obstacles to a successful outcome.