Recent regulations (Reg NMS in the US, MiFID I and II in Europe) put an intensive on electronization of trading, via the use of automated limit orderbooks (See “Market Microstructure in Practice”, S. Laruelle and C.-A. Lehalle Eds. 2013). 
Positive aspects were expected, like an increase of desintermediation and more tracability. Unexpected aspects, like the raise of High Frequency Trading, fragmentation of exchanges and liquidity bifurcation, reshaped the trading process in most developed countries. Market microstructure is now one important topics, intensively monitored by regulators and market participants. 
I will present recent research on orderbooks dynamics to emphasis three different viewpoints on microscopic dynamics: 
* In “Simulating and analyzing order book data: The queue-reactive model” with Weibing Huang and Mathieu Rosenbaum, we started from empirical observation of joint laws of flows on orderbooks, and tried a bottom-up explanation of orderbook dynamics. 
* In another paper “Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis”, with Aimé Lachapelle, Jean-Michel Lasry,and Pierre-Louis Lions, we started from an abstract view of the utility functions of market participants and figured out how stationary joint laws of the quantities on the two sides of the book can emerge.
* The influence of regulation on the orderbooks dynamics is of paramount importance. The most important parameter of the market design is the tick size (i.e. the minimum increment between two consecutive prices). In “How to predict the consequences of a tick value change? Evidence from the Tokyo Stock Exchange pilot program” with Weibing Huang and Mathieu Rosenbaum, we show how our understanding of microstructure enable us to predict the outcome on a tick size change.