What is complexity? A complex system, such as a tropical rainforest, is a tangled web of interactions and exhibits a distinctive property called ‘emergence’, roughly described by ‘the action of the whole is more than the sum of the actions of the parts’. This chapter explains that the interactions of interest are non-linear and thus hierarchical organization is closely tied to emergence. Complex systems explains several kinds of telltale behaviour: emergent behaviour, self-organization, chaotic behaviour, ‘fat-tailed behaviour’, and adaptive interaction. The field of complexity studies has split into two subfields that examine two different kinds of emergence: complex physical systems and complex adaptive systems.