The focus of this thesis is twofold. First, it delivers a new look at existing simulation-based methods for statistical inference in parametric problems. Emphasis is placed on finite sample theoretical properties and computational efficiency. In particular, a simple and computationally efficient method for inference is proposed. It is shown that exact inference may be claimed in theory in some situations even though sample size is kept fixed. Numerical examples demonstrate the wide applicability of this method. Second, a general class of flexible models for dependent random phenomena is studied. Emphasis is placed on problems of point estimations due to the presence of outliers or because of the underlying computational burden. To tackle these issues, a new multi-step robust and computationally efficient estimator is proposed. Asymptotic properties are studied along with illustrative examples.