The notion of polysynthesis has been linked up with that of complexity from the very start. A discussion of the relationship between these two concepts is thus highly motivated, also in view of the recent increased interest in questions relating to complexity among linguists. The chapter discusses different ways of understanding and measuring complexity and how these can be applied to polysynthetic languages. Other topics treated in the chapter are how complexity develops over time in polysynthetic languages, the question of to what extent the notions of maturation and non-linearity as defined in Dahl (2004) are relevant to the synchrony and diachrony of polysynthesis, and how the complexity of constructions in polysynthetic languages compares to functionally equivalent constructions elsewhere.