Nowadays, on more than half of financial markets, trading happens through limit order books. In the first part of my talk, I introduce the limit order book mechanism along with typical quantities such as the bid and ask prices. Using real data, I give some summary statistics, enabling the audience to gain a better intuition about the market dynamics. Moreover, I show an animation of a limit order book, both in real time and slow motion. In the second part, I discuss the limit order book modelling problem and present two main modelling trends: Markov queues and Hawkes processes. I focus on the core ideas behind each model type as well as on their conceptual limitations. I end the talk by briefly explaining the specific problem that I am working on.