Limit order book markets are a rich research area, not only because these markets generated huge amounts of data (at an exceedingly high rate), but also because the fine level of detail that their data enables one to explore market microstructure in unprecedented ways. Due to the large quantity and rich details of the data in such market, one has to leverage the power of computers to perform both the analysis and modeling work. This calls for both new algorithms and infrastructure to perform the computing tasks effectively and efficiently. Motivated by the questions and challenges I see there, I started my research first from a engineering perspective and then moved to a quantitative perspective. My aim was to find my way through this newly emerging area and develop a systematic approach to seek, study and solve the potential questions in it. I will graph and explain my findings and results in this thesis, hoping that they will help and inspire further research work. To discipline and guide myself with a clear goal in the long journey exploring the world of limit order book markets, I focus on liquidity modeling. I try to predict trading volume from a daily scale to intra-day distributions, with the aim to design trading algorithms to reduce transaction costs and market impact. Within a microstructure context, I try to model the self-exciting nature of trading events with both a stochastic process approach and a statistical approach. Prediction methods are proposed to help trading algorithms to react to big trade events in real time. I use two different modelling approaches. One is based on stochastic processes that have nice mathematical properties, while the other one is driven by statistics extracted directly from the data. I try to examine them in a unified and scientific way so that it is easy to compare the strengthes and weaknesses of each of them. Empirical findings are given to support the rationale behind all of the proposed algorithms.