  The paper overviews our recent work on the synthesis of metasurfaces and
related concepts and applications. The synthesis is based on generalized sheet
transition conditions (GSTCs) with a bianisotropic surface susceptibility
tensor model of the metasurface structure. We first place metasurfaces in a
proper historical context and describe the GSTC technique with some fundamental
susceptibility tensor considerations. Upon this basis, we next provide an
in-depth development of our susceptibility-GSTC synthesis technique. Finally,
we present five recent metasurface concepts and applications, which cover the
topics of birefringent transformations, bianisotropic refraction, light
emission enhancement, remote spatial processing and nonlinear second-harmonic
generation.
