  We provide a detailed treatment of Weyl-Titchmarsh theory for half-lattice
and full-lattice Cantero-Moral-Velazquez (CMV) operators and discuss their
systems of orthonormal Laurent polynomials on the unit circle, spectral
functions, variants of Weyl--Titchmarsh functions, and Green's functions. In
particular, we discuss the corresponding spectral representations of
half-lattice and full-lattice CMV operators.
