This chapter discusses some of the most engaging natural phenomena, those in which highly structured collective behavior emerges over time from the interaction of simple subsystems. Emergence is generally understood to be a process that leads to the appearance of structure not directly described by the defining constraints and instantaneous forces which control a system. Over time “something new” appears at scales not directly specified by the equations of motion. An emergent feature also cannot be explicitly represented in the initial (...) and boundary conditions. A feature emerges when the underlying system puts some effort into its creation. These observations form an intuitive definition of emergence. For it to be useful, however, one must specify what the “something” is and in what manner it is “new.” Otherwise, the notion has little or no content, since almost any time-dependent system would exhibit emergent features. (shrink)