  Entropic quantifiers of states lie at the cornerstone of the quantum
information theory. While a quantum state can be abstracted as a device that
only has outputs, the most general quantum device is a quantum channel that
also has inputs. In this work, we extend the entropic quantifiers of states to
the ones of channels. In the one-shot and asymptotic scenarios, we propose
relative entropies of channels under the task of hypothesis testing. Then, we
define the entropy of channels based on relative entropies from the target
channel to the completely depolarising channel. We also study properties of
relative entropies of channels and the interplay with entanglement. Finally,
based on relative entropies of channels, we propose general resource theories
of channels and discuss the coherence of general channels and measurements, and
the entanglement of channels.
