The number of neurons and synapses in biological brains is very large, on the order of millions and billions respectively even in small animals like insects and mice. By comparison most neuronal network models developed and simulated up to now have been tiny, comprising many orders of magnitude less neurons than their real counterpart, with an even more dramatic difference when it comes to the number of synapses. In this chapter we discuss why and when it may be important to work with large-scale, if not full-scale, neuronal network and brain models and to run simulations on supercomputers. We describe the state-of-the-art in large-scale neural simulation technology and methodology as well as ways to analyze and visualize output from such simulations. Finally we discuss the challenges and future trends in this field.