The study of composition operators, most notably on the Hardy space H-2, often leads to issues involving Toeplitz operators acting on that space. Toeplitz operators arise, for example, in Littlewood's original proof that composition operators are bounded on H-2, in the computation of their adjoints, and in questions about their "normality." In addition, there are interesting questions about just how "Toeplitz" a composition operator can be. This article reviews some recent work on these matters.
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