In this paper I review some of the recent advancements in the understanding of the market microstructure of financial markets and of the role of heterogenous investors in explaining the statistical regularities observed in market data. After introducing some of the main problems in microstructure and describing the most common structure of financial markets, the Limit Order Book (LOB), I will focus on the interplay between order flow, describing the intention of the agents, and the price dynamics, describing the outcome of their interactions. I will show that the quantity embedding this subtle interaction, termed market impact, is determined by the large heterogeneity in size of the investors in the financial market. I will also show the relevance of this problem for investors, by introducing the problem of optimal execution and describing the empirical evidences on the associated cost, focusing also on the role of herding behavior. Finally, I will describe some evidences of the role of heterogeneity of time scales in determining some properties of LOB.
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