All the properties that follow:

• A system is complex when it is composed of many parts that interconnect in intricate ways
• A system presents dynamic complexity when cause and effect are subtle, over time.
• A system is complex when it is composed of a group of related units (subsystems), for which the degree and nature of the relationships is imperfectly known. The overall emergent behavior is difficult to predict, even when subsystem behavior is readily predictable. Small changes in inputs or parameters may produce large changes in behavior
• A complex system has a set of different elements so connected or related as to perform a unique function not performable by the elements alone
• Scientific complexity relates to the behavior of macroscopic collections of units endowed with the potential to evolve in time
• Complexity theory and chaos theory both attempt to reconcile the unpredictability of non-linear dynamic systems with a sense of underlying order and structure

make up for this definition I like sooo much:

Complexity is the property of a real world system that is manifest in the inability of any one formalism being adequate to capture all its properties.

Reference

Ferreira, P., 2001. Tracing Complexity Theory. Full presentation available here

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