Hybrid nanostructures are systems composed of two or more nanostructures designed for improving the performance over individual components. In this work we introduce the concept of bridging natural photosynthetic protein-pigment complexes with nanostructures fabricated in an artificial way, such as semiconductor nanocrystals, metallic nanoparticles or carbon nanotubes, with the purpose of enhancing the efficiency of light harvesting either via plasmon excitation in metals or absorption tunability characteristics of semiconductors. In addition to presenting basic features of inorganic nanostructures, we discuss recent advances in the field of hybrid nanostructures composed of photosynthetic pigment-protein complexes.