Recent progress in direct laser writing of three-dimensional (3D) polymer nanostructures for photonics is reviewed. This technology has reached a level of maturity at which it can be considered as the 3D analogue of planar electron-beam lithography. Combined with atomic-layer deposition and/or chemical-vapor deposition of dielectrics—the 3D analogues of planar evaporation technologies, the 3D polymer templates can be converted or inverted into 3D high-refractive-index-contrast nanostructures. Examples discussed in this review include positive and inverse 3D silicon-based woodpile photonic crystals possessing complete photonic bandgaps, novel optical resonator designs within these structures, 3D chiral photonic crystals for polarization-state manipulation, and 3D icosahedral photonic quasicrystals. The latter represent a particularly complex 3D nanostructure.