  I present an overview of some recent advancements on the empirical analysis
and theoretical modeling of the process of price formation in financial markets
as the result of the arrival of orders in a limit order book exchange. After
discussing critically the possible modeling approaches and the observed
stylized facts of order flow, I consider in detail market impact and
transaction cost of trades executed incrementally over an extended period of
time, by comparing model predictions and recent extensive empirical results. I
also discuss how the simultaneous presence of many algorithmic trading
executions affects the quality and cost of trading.
