Dynamic Stochastic General Equilibrium (DSGE) models are an important tool for economists and policymakers. These optimization-based models have an internal coherence that allows one to evaluate policy changes, propagation mechanisms and produce forecasts. Bayesian techniques, in which the likelihood function implied by the model is combined with a prior distribution to yield a posterior distribution for the model parameters, are often used to estimate these models. The focus of this dissertation is developing and applying methodologies for the estimation and evaluation of DSGE models from a Bayesian perspective. The first chapter of this dissertation proposes a block Metropolis-Hastings algorithm for Bayesian estimation of DSGE models as an alternative to current algorithms. The algorithm uses information contained in the gradient and the Hessian of the log posterior to generate proposals via Newton's method. Additionally, parameters are blocked together based on the curvature of the posterior reflected in the Hessian of the log posterior. It is shown that algorithm can more quickly generate independent draws from the posterior. The algorithm is also less likely to get stuck on local modes. The algorithm is applied to several statistical and economic models to highlight these features. The second chapter of this dissertation, based on work with Frank Schorfheide, develops and applies tools to assess multivariate aspects of Bayesian DSGE model forecasts and their ability to predict comovements among key macroeconomic variables. We construct posterior predictive checks to evaluate the calibration of conditional and unconditional density forecasts. The checks are implemented on a three-equation DSGE model as well as the Smets and Wouters (2007) model using real-time data. The additional features incorporated into the Smets-Wouters model do not lead to a uniform improvement in the quality of density forecasts and prediction of comovements of output, inflation, and interest rates. The third chapter of my dissertation uses Bayesian techniques to estimate two versions of a standard New Open Economy model which differ in their treatment of technological change. We find that explicitly incorporating cointegration into technology across countries does not help match the volatility of the real exchange rate in a stylized model.