  We study the intertwining relations between analytic Toeplitz operators
induced on the Hardy space H^2 by analytic functions bounded on the open unit
disc. Our work centers on the connection between intertwining between the
Toeplitz operators the image containment between their symbols, as well as on
the nature of the intertwining operator. We use our results to study the
"extended eigenvalues" of analytic Toeplitz operators, i.e., the special case
where the operator is intertwined with a scalar multiple of itself.
