  Quantum channels are quintessential to quantum information, being used in all
protocols, and describing how systems evolve in space and time. As such, they
play a key role in the manipulation of quantum resources, and they are often
resources themselves, called dynamical resources. This forces us to go beyond
standard resource theories of quantum states. Here we provide a rigorous
foundation for dynamical resource theories, where the resources into play are
quantum channels, explaining how to manipulate dynamical resources with free
superchannels. In particular, when the set of free superchannels is convex, we
present a novel construction of an infinite and complete family of convex
resource monotones, giving necessary and sufficient conditions for
convertibility under free superchannels. After showing that the conversion
problem in convex dynamical resource theories can be solved with conic linear
programming, we define various resource-theoretic protocols for dynamical
resources. These results serve as the framework for the study of concrete
examples of theories of dynamical resources, such as dynamical entanglement
theory.
