Solar cells are a promising renewable, carbon-free electric energy resource to address the fossil fuel shortage and global warming. Energy conversion efficiencies around 40% have been recently achieved in laboratories using III-V semiconductor compounds as photovoltaic materials. This article reviews the efforts and accomplishments made for higher efficiency III-V semiconductor compound solar cells, specifically with multijunction tandem, lower-dimensional, photonic up/down conversion, and plasmonic metallic structures. Technological strategies for further performance improvement from the most efficient (Al)InGaP/(In)GaAs/Ge triple-junction cells including the search for 1.0 eV bandgap semiconductors are discussed. Lower-dimensional systems such as quantum well and dot structures are being intensively studied to realize multiple exciton generation and multiple photon absorption to break the conventional efficiency limit. Implementation of plasmonic metallic nanostructures manipulating photonic energy flow directions to enhance sunlight absorption in thin photovoltaic semiconductor materials is also emerging.