This paper explores Mixed Data Sampling (MIDAS) regression models, which are used to analyze time series data sampled at different frequencies. The authors focus on volatility and related processes, combining recent developments in volatility estimation with literature on distributed lag models. They study various lag structures to parameterize the regressions and propose several new extensions of the MIDAS framework. The paper includes an empirical section that provides further evidence and new results on the risk-return tradeoff and volatility forecasting, particularly in the context of microstructure noise. The authors also discuss the flexibility and advantages of MIDAS models, including their ability to capture rich dynamics with parsimonious parameterizations. They explore different polynomial specifications, such as finite and infinite polynomials, stepfunctions, and non-linear MIDAS regressions. The paper concludes with a discussion of multivariate MIDAS regression models and their potential applications in volatility forecasting and Granger causality testing.This paper explores Mixed Data Sampling (MIDAS) regression models, which are used to analyze time series data sampled at different frequencies. The authors focus on volatility and related processes, combining recent developments in volatility estimation with literature on distributed lag models. They study various lag structures to parameterize the regressions and propose several new extensions of the MIDAS framework. The paper includes an empirical section that provides further evidence and new results on the risk-return tradeoff and volatility forecasting, particularly in the context of microstructure noise. The authors also discuss the flexibility and advantages of MIDAS models, including their ability to capture rich dynamics with parsimonious parameterizations. They explore different polynomial specifications, such as finite and infinite polynomials, stepfunctions, and non-linear MIDAS regressions. The paper concludes with a discussion of multivariate MIDAS regression models and their potential applications in volatility forecasting and Granger causality testing.