This paper argues for a "human-centered" approach to knowledge discovery from movement data through the use of visualization and mapping. As movement data becomes more available and diverse in dimension and resolution, mapping becomes particularly important in the exploratory analysis of movement trajectories and for capturing patterns and structures in large origindestination flow data sets. Movement phenomena (e.g. ranging from micro-movements of humans and animals to macro-level mobility, to migration flows, to spread of viruses) are complex dynamic processes which are realized in a multidimensional location-time-context space. This paper provides a comprehensive overview of various visualization techniques for mapping movement through the lens of cartography and with a special focus on the "human user" (e.g. data scientist, analyst, domain expert, etc.). We systematically characterize and categorize available techniques based on their visual specifications and functional capacities for human control, map-interaction, and design flexibility. These elements are beneficial to enhance the user's capacities for map reasoning and knowledge discovery. Trends and gaps in the literature on movement visualization over the past 10 years are discussed. Our review suggests that future research should focus more on the role of the "human" in the development of human-centered visual analytic and exploratory tools, while providing functionalities for mapping uncertainty and protecting individual privacy in knowledge discovery of movement. These tools should be guided by a cartographic framework and visual principles specifically pertinent to movement.