Millimeter wave (MMW) GRadient INdex (GRIN) lens antennas leverage spatially varying refractive structures to generate high directivity beams. GRIN lenses also demonstrate high aperture efficiency over beam-scan and can be made relatively low-profile by using high permittivity, low-loss dielectric materials. Most importantly, GRIN lenses have uniquely high instantaneous bandwidth and low power consumption compared to incumbent beam-scanning antenna technologies. These characteristics overall make GRIN lens antennas compelling for applications like MMW 5G and low earth orbit (LEO) satellite communications that require low-power, high performance beam-scanning antenna systems. Unfortunately, the features that GRIN lens antennas demonstrate in aggregate are difficult to synthesize in a single system. The goal of this thesis is to provide a framework for designing flat GRIN lens systems that simultaneously demonstrate high instantaneous bandwidth, high aperture efficiency, and high beam-scanning capability in a practical form-factor.First, a flat GRIN lens morphology is proposed. While spherical systems like the Luneburg lens demonstrate near-perfect beam-scanning performance with high aperture efficiency, the curved focal surface and overall bulk of these systems makes them impractical. We identify two primary research tasks: 1) designing flat lens systems with high aperture efficiency over a wide bandwidth and 2) designing flat lens systems with wide-angle beam-scanning. We address research objective #1 by first noting that the bandwidth of flat lens systems is constrained by the impedance matching layers at the lens boundary. We then demonstrate a X-band to Ka-band flat GRIN lens using intrinsically wideband matched unit-cells. The measured aperture efficiency ranges from 31% to 71% over a 2.9:1 bandwidth; at the time of writing this is the highest aperture efficiency demonstrated across such a wide bandwidth.We address research objective #2 by characterizing the scan loss in flat focal surface systems and determining that wide-angle scan loss is dominated by spillover and taper losses associated with far-offset feed positions. We then propose the use of additional GRIN structures near the focal surface to reduce scan loss and demonstrate two systems with improved scan loss. The second of these — a full compound GRIN lens — demonstrates a measured scan loss exponent of ns = 1.5 over a ±48degree field of view at 40 GHz while requiring only 37.3% of the total material that would be required for a comparably sized Luneburg lens.