In recent years we have observed an unprecedented growth in the complexity of instruments for trading and risk management in international markets. The growth in complexity has been accompanied by an expanded role of mathematical models to value these instruments and to measure their risks. In the midst of this, models for high-frequency data have increasingly been playing a predominant role. High frequency data modeling in finance was traditionally viewed as a combination of observed empirical facts, market micro-structure theory, and econometrics. Market micro-structure theory aims at constructing models explaining market participants behavior under prescribed market rules and conditions (e.g,with/without market maker, with/without order books, opening and closing hours, maximum price variations, minimum traded volume, etc.). Empirical research analyze the constructed models to assess their feasibility by, for instance, verifying that their output and properties match those of real financial data. Thus, the analysis of high frequency data seeks to answer questions that are fundamental to policy makers. For example, how much information should regulators disclose to market participants, how do extreme movements in the order book affect market liquidity, is a market maker really necessary, and many others. At the same time, practitioners, who are traders that participate in the market every day, also have an interest in understanding financial markets that operate at high frequency. For instance, trading rules may be constructed based on the markets conditions that, in turn, may be justied by financial econometrics. These rules however apply to industry participants who have to have an input to void destabilizing the market.