  The capacity of distant parties to send signals to one another is a
fundamental requirement in many information-processing tasks. Such ability is
determined by the causal structure connecting the parties, and more generally,
by the intermediate processes carrying signals from one laboratory to another.
Here we build a fully fledged resource theory of causal connection for all
multi-party communication scenarios, encompassing those where the parties
operate in a definite causal order and also where the order is indefinite. We
define and characterize the set of free processes and three different sets of
free transformations thereof, resulting in three distinct resource theories of
causal connection. In the causally ordered setting, we identify the most
resourceful processes in the bipartite and tripartite scenarios. In the general
setting, instead, our results suggest that there is no global most valuable
resource. We establish the signalling robustness as a resource monotone of
causal connection and provide tight bounds on it for many pertinent sets of
processes. Finally, we introduce a resource theory of causal non-separability,
and show that it is -- in contrast to the case of causal connection -- unique.
Together our results offer a flexible and comprehensive framework to quantify
and transform general quantum processes, as well as insights into their
multi-layered causal connection structures.
