Despite extensive research efforts in recent years, computational argumentation (CA) remains one of the most challenging areas of natural language processing. The reason for this is the inherent complexity of the cognitive processes behind human argumentation, which integrate a plethora of different types of knowledge, ranging from topic-specific facts and common sense to rhetorical knowledge. The integration of knowledge from such a wide range in CA requires modeling capabilities far beyond many other natural language understanding tasks. Existing research on mining, assessing, reasoning over, and generating arguments largely acknowledges that much more knowledge is needed to accurately model argumentation computationally. However, a systematic overview of the types of knowledge introduced in existing CA models is missing, hindering targeted progress in the field. Adopting the operational definition of knowledge as any task-relevant normative information not provided as input, the survey paper at hand fills this gap by (1) proposing a taxonomy of types of knowledge required in CA tasks, (2) systematizing the large body of CA work according to the reliance on and exploitation of these knowledge types for the four main research areas in CA, and (3) outlining and discussing directions for future research efforts in CA.