Limit order books (LOBs) match buyers and sellers in more than half of the world's
financial markets. This survey highlights the insights that have emerged from the
wealth of empirical and theoretical studies of LOBs. We examine the findings reported
by statistical analyses of historical LOB data and discuss how several LOB models
provide insight into certain aspects of the mechanism. We also illustrate that many
such models poorly resemble real LOBs and that several well-established empirical
facts have yet to be reproduced satisfactorily. Finally, we identify several key unresolved
questions about LOBs.