  The nonlocal world presents an abundance of surprises and wonders to
discover. These special properties of the nonlocal world are usually the
consequence of long-range interactions, which, especially in presence of
geometric structures and nonlinear phenomena, end up producing a variety of
novel patterns. We will briefly discuss some of these features, focusing on the
case of (non)local minimal surfaces, (non)local phase coexistence models, and
(non)local geometric flows.
