Controlling the directivity of emission and absorption at the nanoscale holds great promise for improving the performance of optoelectronic devices. Previously, directive structures have largely been centered in two categories—nanoscale antennas, and classical lenses. Herein, we utilize an evolutionary algorithm to design 3D dielectric nanophotonic lens structures leveraging both the interference-based control of antennas and the broadband operation of lenses. By sculpting the dielectric environment around an emitter, these nanolenses achieve directivities of 101 for point-sources, and 67 for finite-source nanowire emitters; 3× greater than that of a traditional spherical lens with nearly constant performance over a 200 nm wavelength range. The nanolenses are experimentally fabricated on GaAs nanowires, and characterized via photoluminescence Fourier microscopy, with an observed beaming half-angle of 3.5° and a measured directivity of 22. Simulations attribute the main limitation in the obtained directivity to imperfect alignment of the nanolens to the nanowire beneath.