  In the context of characterizing the structure of quantum entanglement in
many-body systems, we introduce the entanglement contour, a tool to identify
which real-space degrees of freedom contribute, and how much, to the
entanglement of a region A with the rest of the system B. The entanglement
contour provides a complementary, more refined approach to characterizing
entanglement than just considering the entanglement entropy between A and B,
with several concrete advantages. We illustrate this in the context of ground
states and quantum quenches in fermionic quadratic systems. For instance, in a
quantum critical system in $D = 1$ spatial dimensions, the entanglement contour
allows us to determine the central charge of the underlying conformal field
theory from just a single partition of the system into regions A and B, (using
the entanglement entropy for the same task requires considering several
partitions). In $D \geq 2$ dimensions, the entanglement contour can distinguish
between gapped and gapless phases that obey a same boundary law for
entanglement entropy. During a local or global quantum quench, the
time-dependent contour provides a detailed account of the dynamics of
entanglement, including propagating entanglement waves, which offers a
microscopic explanation of the behavior of the entanglement entropy as a
function of time.
