This chapter aims to fill a gap concerning a significant pillar of plasma physics. This can only be achieved very incompletely, as complex plasmas (also referred to as dusty, non-ideal, or colloidal)PlasmacomplexPlasmadustyPlasmanon-idealPlasmacolloidal would deserve a much broader scope if one were to do justice to their rapid development, both scientifically and technologically. But as with magnetic confinement (Chap.  10 ) and laser plasmas (Chap.  11 ), this is a vast field that can only be fully covered in specialized books. (The fact that the chapter on “Complex Plasmas” is shorter than the two preceding ones is also—unintentionally—due to the fact that complex plasmas are not the author’s main research focus. However, the brevity is by no means intended to signal lesser importance.) The idea behind including it here is to show how such a research field builds upon the fundamentals presented in Part I. We choose three examples for demonstration: charging of heavy dust particles, a new oscillation mode that appears due to the presence of a third component in the plasma, and crystallization, when we can no longer speak of ideal plasma situationsDust acoustic modeCrystallizationCharging.