On a nutritional standpoint, lipids are now being studied beyond their energy content and fatty acid (FA) profiles. Dietary FA are building blocks of a huge diversity of more complex molecules such as triacylglycerols (TAG) and phospholipids (PL), themselves organised in supramolecular structures presenting different thermal behaviours. They are generally embedded in complex food matrixes. Recent reports have revealed that molecular and supramolecular structures of lipids and their liquid or solid state at the body temperature influence both the digestibility and metabolism of dietary FA. The aim of the present review is to highlight recent knowledge on the impact on FA digestion, absorption and metabolism of: (i) the intramolecular structure of TAG; (ii) the nature of the lipid molecules carrying FA; (iii) the supramolecular organization and physical state of lipids in native and formulated food products and (iv) the food matrix. Further work should be accomplished now to obtain a more reliable body of evidence and integrate these data in future dietary recommendations. Additionally, innovative lipid formulations in which the health beneficial effects of either native or recomposed structures of lipids will be taken into account can be foreseen.