Does biological computation happen at some sort of "edge of chaos", a dynamical regime somewhere between order and chaos? And if so, is this a fundamental principle that underlies self-organization, evolution, and complex natural and artificial systems that are subjected to adaptation? In this article, we will review the literature on the fundamental principles of computation in natural and artificial systems at the "edge of chaos". The term was coined by Norman Packard in the late 1980s. Since then, the concept of "adaptation to the edge of chaos" was demonstrated and investigated in many fields where both simple and complex systems receive some sort of feedback. Besides reviewing both historic and recent literature, we will also review critical voices of the concept.