It is well established that visualization is of paramount importance to individual and collective cognition, understanding, imagination, innovation, and knowledge creation. This paper explores the research, theory, and practice that helps us to define and explicate the processes of Systems Mapping. It provides three critical insights: (1) that "visualizing" is a proxy for numerous other functional operations such as: tactile or tangible manipulation and movement; object-orientation; social navigation; and, embodied learning; (2) that any definition of Systems Mapping that does not include an explication of the implicit cognitive structures is lacking; and, (3) that Systems Mapping, like Systems Thinking, must be derived from a universal cognitive grammar (UCG) that parallels physical structures in the universe. The paper concludes that a Rubric to Evaluate Systems Mapping Tools is needed to assess the necessary and sufficient features of any Systems mapping medium (i.e., internal thought, white or blackboarding, tactile manipulatives, software, group process, etc).