Innovations in data visualization punctuate the landmark advances in human connectome research since its beginnings. From tensor glyphs for diffusion-weighted imaging, to advanced rendering of anatomical tracts, to more recent graph-based representations of functional connectivity data, many of the ways we have come to understand the human connectome are through the intuitive insight these visualizations enable. Nonetheless, several unresolved problems persist. For example, probabilistic tractography lacks the visual appeal of its deterministic equivalent, multimodal representations require extreme levels of data reduction, and rendering the full connectome within an anatomical space makes the contents cluttered and unreadable. In part, these challenges require compromises between several tensions that determine connectome visualization practice, such as prioritizing anatomic or connectomic information, aesthetic appeal or information content, and thoroughness or readability. To illustrate the ongoing negotiation between these priorities, we provide an overview of various visualization methods that have evolved for anatomical and functional connectivity data. We then describe interactive visualization tools currently available for use in research, and we conclude with concerns and developments in the presentation of connectivity results.