Despite numerous experimental and theoretical studies reported in the literature, surface micro-texturing to control friction and wear in lubricated tribo-contacts is still in the trial-and-error phase. The tribological behaviour and advantageous micro-texture geometries and arrangements largely depend on the contact type and the operating conditions. Industrial scale implementation is hampered by the complexity of numerical approaches. This substantiates the urgent need to numerically design and optimize micro-textures for specific conditions. Since these aspects have not been covered by other review articles yet, we aim at summarizing the existing state-of-the art regarding optimization strategies for micro-textures applied in hydrodynamically and elastohydrodynamically lubricated contacts. Our analysis demonstrates the great potential of optimization strategies to further tailor micro-textures with the overall aim to reduce friction and wear, thus contributing toward an improved energy efficiency and sustainability.