This work reviews the main univariate and multivariate models proposed in the literature to represent the second moments dynamics. The paper starts with a description of stylized facts of financial time series and follows with a comparative study of different models available for modelling these characteristics. The main statistical properties of ARCH and stochastic volatility models are analyzed, as well as, the state space models with dynamics in the variance, Markow switching-variance models and microstructure models. Bayesian contributions to the field are also reviewed
