New-Keynesian Dynamic Stochastic General Equilibrium (DSGE) models are important tools for analyzing modern monetary economics and policy. The genre of the New-Keynesian DSGE model is divided into two broad categories. These are,(i) the sticky price New-Keynesian DSGE model and (ii) the sticky information New-Keynesian DSGE model. My dissertation is a contribution to this rapidly growing literature, where I have analyzed some important issues of modern monetary economics and policy through the New-Keynesian DSGE models.