We present our latest advances in antenna miniaturization using dielectric resonators and design of sparse arrays for ultra-wide band applications without the need for non-linear numerical optimization. We experimentally demonstrate a dualfeed, low-profile, stacked dielectric resonator antenna for the C band with wide bandwidth and high gain, as well as a bio-inspired sparse array design for ultra-wide band applications. We show that the results presented can be successfully extended to other frequency windows, in particular the near-infrared range, where specific issues prevent the use of more conventional antenna and antenna array designs.