For questions about interpolation of operators. This includes: real and complex interpolation, interpolation estimates, interpolation spaces. Questions about the estimation of a function from a given input should be asked under the [interpolation] tag instead.
Interpolation theorems are a class of results which can be broadly characterized as follows: given information about an operator defined on two different "endpoint" cases, one can deduce information about the behavior of the operator in "intermediate" cases. Notable results in this vein include the Riesz-Thorin theorem and the Marcinkiewicz interpolation theorem.
Interpolation theorems serve an important role in the fields of analysis and partial differential equations. In these contexts one might study particular interpolation results that are appropriate for the given context. One may also study interpolation more abstractly, in the form of interpolation spaces and functors.
Interpolation theory is sometimes referred to as "interpolation of operators" to distinguish it from "interpolation of functions," in which one approximates a function given partial information about its values: interpolation.