The analysis of massive, high-volume data sets stresses usual statistical software systems and requires new ways of drawing inferences beyond the conventional paradigm (optimal estimation of parameters from a hypothesized distribution), since the entire data set often cannot be read into the software system. Internet traffic data raise additional challenges: nearly continuous streams of observations from multiple computer systems that interact and exchange information in nondeterministic ways. These features invite cyber attacks, which can be introduced and spread rapidly, and which thus require methods that can detect very rapidly potential departures from "typical" behavior. This talk presents a variety of "visual analytics", graphical displays from which inferences about both "typical" and "exotic" behavior can be observed quickly by the novice user. Statisticians must be involved in the development of these displays, with attention to the needs and abilities of the people who will rely on them to detect cyberattacks. We describe components of internet traffic, propose some methods of visualizing them, and illustrate these methods on data collected at a university network. Some open problems in studying high-volume data in general are mentioned.