  The paper describes various approaches to the invertibility of Toeplitz plus
Hankel operators in Hardy and $l^p$-spaces, integral and difference Wiener-Hopf
plus Hankel operators and generalized Toeplitz plus Hankel operators. Special
attention is paid to a newly developed method, which allows to establish
necessary, sufficient and also necessary and sufficient conditions of
invertibility, one-sided and generalized invertibility for wide classes of
operators and derive efficient formulas for the corresponding inverses. The
work also contains a number of problems whose solution would be of interest in
both theoretical and applied contexts.
