  In the recent decade, the research field using arrays of high-index-contrast
near-wavelength dieletric structures on flat surfaces, known as high-contrast
metastructures (HCMs) or metasurfaces, has emerged and expanded rapidly.
Although the HCMs and metasurfaces share great similarities in physical
structures with photonic crystals (PhCs), i.e. periodic nanostructures, many
differences exist in their design, analysis, operation conditions, and
applications. In this paper, we provide a generalized theoretical understanding
of the two subjects and show their intrinsic connections. We further discuss
the simulation and design approaches, categorized by their functionalities and
applications. The similarity and differences between HCMs, metasurfaces and
PhCs are also discussed. New findings are presented regarding the physical
connection between the PhC band structures and the 1D and 2D HCM scattering
spectra under transverse and longitudinal tilt incidence. Novel designs using
HCMs as holograms, spatial light modulators, and surface plasmonic couplers are
discussed. Recent advances on HCMs, metasurfaces and PhCs are reviewed and
compared for applications such as broadband mirrors, waveguides, couplers,
resonators, and reconfigurable optics.
