Existing surveys in visual analytics focus on the importance of the topic. However, many do not discuss the increasingly critical area of mixed-initiative systems. In this survey we discuss the importance of research in mixed-initiative systems and how it is different from visual analytics and other research fields. We present the conceptual architecture of a mixed-initiative visual analytics system (MIVAS) and the five key components that make up MIVASs (data wrangling, alternative discovery and comparison, parametric interaction, history tracking and exploration, and system agency and adaptation), which forms our main contribution. We compare and contrast different research that claims to be mixed-initiative against MIVASs and show how there is still a considerable amount of work that needs to be accomplished before any system can truly be mixed-initiative.