Photon sieves composed of etched holes on an opaque film have been proposed firstly, to the best of our knowledge, to reduce the focal spot size and alleviate high diffraction orders in soft X-ray and the optical spectrum. With the rapid development of nano-fabrication technology, photon sieves have been demonstrated at nanoscale and worked as binary-amplitude metasurfaces for optical focusing. The photon nanosieves have the advantages of polarization independence and more degrees of freedom in design than the concentric rings in zone plates, which therefore enable more complex manipulation of light, such as hologram, by arranging the locations of holes in a customized way. Due to the subwavelength feature of nanosieves, their related holograms usually support broadband operation. In addition, the non-resonating mechanism of amplitude modulation makes the nanosieve hologram have a wider spectrum than other metasurface devices with resonating nano-structures. The nanosieve hologram also enables a large field of view for holographic display when combined with tunable phase realized by a spatial light modulator. Beyond the circular shape, rectangle nanosieves have also been proposed to control the geometric phase of a circularly polarized light by rotating the orientations of the rectangular nanosieves, thus enabling full-color holography and the generation of optical vortices in various electromagnetic spectra such as X-ray and vacuum ultraviolet wavelengths.