Miniaturization of optical structures makes it possible to control light at the nanoscale, but on the other hand it imposes a challenge of accurately handling numerous unit elements in a miniaturized device with aperiodic and random arrangements. Here, we report both the new analytical model and experimental demonstration of the photon sieves with ultrahighcapacity of subwavelength holes (over 34 thousands) arranged in two different structural orders of randomness and aperiodicity. The random photon sieve produces a uniform optical hologram with high diffraction efficiency and free from twin images that are usually seen in
conventional holography, while the aperiodic photon sieve manifests sub-diffraction-limit focusing in air. A hybrid approach is developed to make the design of random and aperiodic photon sieve viable for high-accuracy control of the amplitude, phase and polarization of visible light. The polarization independence of the photon sieve will also greatly benefit its applications in optical imaging and spectroscopy.