This presentation summarizes the development and implementation of quantitative design criteria motivated by targeted inference objectives for identifying new, potentially expensive computational or physical experiments. The first application is concerned with estimating features of quantities of interest arising from complex computational models, such as quantiles or failure probabilities. A sequential strategy is proposed for iterative refinement of the importance distributons used to efficiently sample the uncertain inputs to the computational model. In the second application, effective use of mathematical surrogates is investigated to help alleviate the analytical and numerical intractability often associated with Bayesian experiment design. This approach allows for the incorporation of prior information into the design process without the need for gross simplification of the design criterion. Illustrative examples of both design problems will be presented as an argument for the relevance of these research problems.