The aim of this thesis is to present and investigate the methodology of Durbin and Koopman (DK) used to estimate non-Gaussian state space time series models, within the context of structural models. DK`s approach is based on evaluating the likelihood using efficient Monte Carlo simulation, by means of importance sampling and variance- reduction techniques, such as antithetic variables and control variables. It also contents known existent techniques for the Gaussian case as the Kalman Filter smoother Simulation algorithm. Once the model hyperparameters are estimated, the state, which encapsulates the model`s components, is estimated by evaluating its posterior mode. Proposals are approximated to evaluate mean and variance for the predictive distribution. Applications are considered using the Poisson model.