  We present a general methodology for electromagnetic homogenization and
characterization of bianisotropic metasurfaces formed by regular or random
arrangements of small arbitrary inclusions at the interface of two different
isotropic media. These topologies can provide the most general electric and
magnetic surface-bound dipolar responses to incident electromagnetic waves. The
approach unites and generalizes the earlier theories developed independently by
two research groups: the joint group of profs. Holloway and Kuester and the
joint group of profs. Simovski and Tretyakov. We demonstrate the use of both
formalisms in several example cases and discuss the differences between the two
approaches. Furthermore, we generalize the known theories for the bianisotropic
metasurfaces located at interfaces between two different media or on a
substrate. The generalized framework allows characterization of both periodical
or amorphous metasurfaces. The developed analytical theory can be used in the
analysis and synthesis of metasurfaces for a wide variety of applications.
