  Bell's Theorem witnesses that the predictions of quantum theory cannot be
reproduced by theories of local hidden variables in which observers can choose
their measurements independently of the source. Working out an idea of
Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature
several sources, but no choice of measurement for the observers. Every Bell
scenario can be mapped into such a \emph{correlation scenario}, and Bell's
Theorem then discards those local hidden variable theories in which the sources
are independent. However, most correlation scenarios do not arise from Bell
scenarios, and we describe examples of (quantum) nonlocality in some of these
scenarios, while posing many open problems along the way. Some of our scenarios
have been considered before by mathematicians in the context of causal
inference.
