In this paper, a New-Keynesian DSGE model for a small open economy integrated in a monetary union is developed and estimated for the Portuguese economy, using a Bayesian approach. Estimates for some key structural parameters are obtained and a set of exercises exploring the model's empirical properties and the results' robustness are performed. A survey on the main events and literature associated with DSGE models is also provided, as well as a comprehensive discussion of Bayesian estimation and model comparison techniques. The model features five types of economic agents namely households, firms, aggregators, the rest of the world and the government, and includes a number of shocks and frictions, which enable a closer matching of the short-run properties of the data and a more realistic short- term adjustment to shocks. It is assumed from the outset that monetary policy is defined by the union's central bank and that the domestic economy's size is negligible, relative to the union's one, and therefore its specific economic fluctuations have no influence on the union's macroeconomic aggregates and monetary policy. A risk-premium is considered, to allow for deviations of the domestic economy's interest rate from the union's one. Furthermore it is assumed that all trade and financial flows are performed with countries belonging to the union, which implies that the nominal exchange rate is irrevocably set to unity.