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Chirality - handedness - is everywhere. Snail shells run clockwise or anti-clockwise. Optical activity caused by chiral molecules was discovered at the beginning of the 19th century when studying light passing through liquid solutions of sugar. The development of artificial chiral materials attracts the attention of research in the field of inverse scattering problems. This work deals with several aspects of inverse scattering for inhomogeneous chiral materials: A chiral object - the scatterer - is situated in vacuum and illuminated by an electromagnetic wave. This wave is scattered. The direct problem is to compute the scattered wave for a given incident wave and a given chiral object. The inverse problem is to determine the scatterer from information about the scattered field. The Factorization Method is generalized to inverse scattering problems for Maxwell's equations in combination with the Drude-Born-Fedorov constitutive relations as well as for the 2D vector Helmholtz equation. It provides a necessary and sufficient criterion to determine the characteristic function of the scatterer and overcomes the disadvantages of other solving methods.