  It was recently realised that quantum theory allows for so-called causally
nonseparable processes, which are incompatible with any definite causal order.
This was first suggested on a rather abstract level by the formalism of process
matrices, which only assumes that quantum theory holds locally in some
observers' laboratories, but does not impose a global causal structure; it was
then shown, on a more practical level, that the quantum switch---a new resource
for quantum computation that goes beyond causally ordered circuits---provided
precisely a physical example of a causally nonseparable process. To demonstrate
that a given process is causally nonseparable, we introduced in [Ara\'ujo et
al., New J. Phys. 17, 102001 (2015)] the concept of witnesses of causal
nonseparability. Here we present a shorter introduction to this concept, and
concentrate on some explicit examples to show how to construct and use such
witnesses in practice.
