This book provides a methodological framework to model univariate and multivariate irregularly spaced financial data. It gives a thorough review of recent developments in the econometric literature, puts forward existing approaches and opens up new directions. The book presents alternative ways to model so-called financial point processes using dynamic duration as well as intensity models and discusses their ability to account for specific features of point process data, like the occurrence of time-varying covariates, censoring mechanisms and multivariate structures. Moreover, it illustrates the use of various types of financial point processes to model financial market activity from different viewpoints and to construct volatility and liquidity measures under explicit consideration of the passing trading time.