The GLEAMviz simulator is a scientific application designed for researchers and students in the field of epidemiology, who are interested in performing realistic simulations of the spreading of infectious diseases on a global scale. The system consists of a server component, whose computational engine uses the Global Epidemic and Mobility (GLEAM) model, and a desktop client software, that can be used to set up simulations with an intuitive visual user interface, and to explore the results by means of various analysis tools. The GLEAMviz client, freely available, allows users to develop arbitrary disease models, to interact with the server for executing the simulations, and to visualize the output using maps, charts and other powerful widgets.