The vascular anatomy of the liver can be described at three different levels of complexity according to the use that the description has to serve. The first--conventional--level corresponds to the traditional 8-segments scheme of Couinaud and serves as a common language between clinicians from different specialties to describe the location of focal hepatic lesions. The second--surgical--level, to be applied to anatomical liver resections and transplantations, takes into account the real branching of the major portal pedicles and of the hepatic veins. Radiological and surgical techniques exist nowadays to make full use of this anatomy, but this requires accepting that the Couinaud scheme is a simplification, and looking at the vascular architecture with an unprejudiced eye. The third--academic--level of complexity concerns the anatomist, and the need to offer a systematization that resolves the apparent contradictions between anatomical literature, radiological imaging, and surgical practice. Based on the real number of second-order portal branches that, although variable averages 20, we submit a system called the "1-2-20 concept", and suggest that it fits best the number of actual--as opposed to idealized--anatomical liver segments.