Some elemental liquids (e.g. Sb, Bi, Se, Te) display anomalous, “water-like” physical properties, including: (i) melting curves which decrease with pressure (ii) sound velocities that increase with temperature (iii) densities that increase with temperature. Hypothesising that these phenomena originate from the structure of the liquid, we search for structural manifestation of these properties. Analysis of the radial distribution function leads to questions regarding the structure of the liquid and its interpretation which are considered within the quasi-crystalline model of the liquid structure. In analogy with water, it has been suggested that the origin of these anomalous physical properties lies in the existence of a (inaccessible?) liquid-liquid critical point in the metastable, super-cooled region of the liquid phase diagram. The recognition of the possible existence of first order liquid-liquid phase transitions in elemental liquids has been one of the most exciting developments in liquid physics in recent years. However, the direct experimental identification and verification of such transitions is a great challenge. Possible signatures of such liquid-liquid phase transitions in the structure, thermophysical properties and phase diagrams of liquid metals are explored.