Complexity is a matter of distance

Complex systems constitute a cross-disciplinary field that studies natural and societal phenomena. In general, complexity relates to different aspects of a system, such as emergent behaviours, interaction patterns, and other properties. Also, complexity can refer to the resources required to accomplish a task. Here, we review a limited collection of methods for studying complexity across different topics. The resulting picture highlights interesting relationships between complexity and distance, showing up in all considered systems, from phase transitions to black hole evolution. We conclude by discussing related implications and a few examples beyond Physics that corroborate the validity of the highlighted relationships.