The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This talk will present two distinct classifications addressing commutant lifting in the polydisc setting. The first classification links the lifting problem to the contractivity of certain linear functionals. The second classification reformulates the lifting problem in terms of nonnegative real numbers. We will also solve the Nevanlinna-Pick type interpolation problem for bounded analytic functions on the polydisc. If time permits, we will talk about a solution to a perturbation problem for bounded analytic functions. This talk is based on joint work with Deepak K. D.

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