To describe certain facets of nonclassicality, it is necessary to quantify properties of operations instead of
states. This is the case if one wants to quantify how well an operation detects nonclassicality, which is a
necessary prerequisite for its use in quantum technologies. To do so rigorously, we build resource theories
on the level of operations, exploiting the concept of resource destroying maps. We discuss the two basic
ingredients of these resource theories, the free operations and the free superoperations, which are sequential
and parallel concatenations with free operations. This leads to defining properties of functionals that are
well suited to quantify the resources of operations. We introduce these concepts at the example of
coherence. In particular, we present two measures quantifying the ability of an operation to detect, i.e., to
use, coherence, one of them with an operational interpretation, and provide methods to evaluate them.