The concept of project complexity has evolved a tremendously since topic discussions were initiated. A diversification was sparked a decade ago. The multiplicity of concepts makes it increasingly challenging to utilize the overall research stream of project complexity. This paper takes stock and presents a typology with five ideal types of research in project complexity. This demonstrate an overarching relation between the type of research of project complexity and the inherent perspective on project success. The typology contributes a much-needed overview for researchers who are new to the overall topic of project complexity. The complexity of projects is an important aspect of research of rethinking of project management, and the typology has the potential of forming a theory of project complexity supporting this research.