Optical metasurfaces are a category of thin diffractive optical elements, fabricated using the standard micro- and nano-fabrication techniques. They provide new ways of controlling the flow of light based on various properties such as polarization, wavelength, and propagation direction. In addition, their compatibility with standard micro-fabrication techniques and compact form factor allows for the development of several novel platforms for the design and implementation of various complicated optical elements and systems. In this thesis, I first give a short overview and a brief history of the works on optical metasurfaces. Then I discuss the capabilities of metasurfaces in controlling the polarization and phase of light, and showcase their potential applications through the cases of polarimetric imaging and vectorial holography. Then, a discussion of the chromatic dispersion in optical metasurfaces is given, followed by three methods that can be utilized to design metasurfaces working at multiple discrete wavelengths. As a potential application of such metasurfaces, I present results of using them as objective lenses in two-photon microscopy. In addition, I discuss how metasurfaces enable the at-will control of chromatic dispersion in diffractive optical elements, demonstrate metasurfaces with controlled dispersion, and provide a discussion of their limitations. Integration of multiple metasurfaces into metasystems allows for implementation of complicated optical functions such as imaging and spectrometry. In this regard, I present several examples of how such metasystems can be designed, fabricated, and utilized to provide wide field of view imaging and projection, microelectromechanically tunable lenses, optical spectrometers, and retroreflectors. I conclude with an outlook on where metasurfaces can be most useful, and what limitations should be overcome before they can find wide-spread application.</p
