This article explores the statistical treatment and estimation of multivariate stochastic variance models, which are used to model changes in variance or volatility over time. The authors discuss the challenges of estimating and interpreting these models, particularly in the context of financial time series such as stock returns and exchange rates. They introduce the concept of modeling variance as an unobserved stochastic process, which is closely linked to developments in finance theory. The article reviews univariate GARCH and SV models, compares their properties, and discusses the estimation of SV models using quasi-maximum likelihood. It then extends these models to multivariate series, showing how they can capture common movements in volatility. The authors present an empirical application to daily exchange rates, demonstrating the model's ability to fit real data and identify common factors. Finally, they discuss the extension of the model to heavy-tailed distributions, using the Student's t-distribution. The article concludes by highlighting the natural interpretation and parsimony of the multivariate stochastic variance model, its ease of estimation, and its effectiveness in capturing common volatility movements.This article explores the statistical treatment and estimation of multivariate stochastic variance models, which are used to model changes in variance or volatility over time. The authors discuss the challenges of estimating and interpreting these models, particularly in the context of financial time series such as stock returns and exchange rates. They introduce the concept of modeling variance as an unobserved stochastic process, which is closely linked to developments in finance theory. The article reviews univariate GARCH and SV models, compares their properties, and discusses the estimation of SV models using quasi-maximum likelihood. It then extends these models to multivariate series, showing how they can capture common movements in volatility. The authors present an empirical application to daily exchange rates, demonstrating the model's ability to fit real data and identify common factors. Finally, they discuss the extension of the model to heavy-tailed distributions, using the Student's t-distribution. The article concludes by highlighting the natural interpretation and parsimony of the multivariate stochastic variance model, its ease of estimation, and its effectiveness in capturing common volatility movements.