Model spaces can be seen as particular cases of Toeplitz kernels or kernels of truncated Toeplitz operators. In this talk we discuss how various properties of model spaces, in particular orthogonal decompositions, can be extended to the kernels of several classes of general Wiener-Hopf operators, including Toeplitz operators and truncated Toeplitz operators.

Based on joint work with Marek Ptak and Kamila Klis-Garlicka.