With the movement away from the trading floor to electronic exchanges and the accompanying substantial increase in the volume of order submission has come the need for tractable mathematical models of the evolution of the limit-order book. The problem is inherently high dimensional, and any realistic description of order flows must have them depend on the state of the limit-order book. Poisson process models for the evolution of the limit-order book have been proposed, but the analysis of these is either difficult or impossible. In this talk, we show how diffusion scaling of a simple Poisson model, inspired by queueing theory, can lead to a rich yet tractable diffusion model for the evolution of the limit-order book. We then show how to compute the probability of up and down price moves and the time between price changes in this model. This is joint work with Chris Almost, John Lehoczky and Xiaofeng Yu.