Recently many regularized estimators have been proposed and applied to capture various types of structural parsimony in high-dimensional applications. Yet with multiple sparsity-promoting penalties or constraints enforced on the same object, sharp theoretical results become difficult to obtain. In particular, there is a lack of systematic finite-sample studies in the literature. This talk presents some nonasymptotic results based on two novel recipes. They are both based on combined computational and statistical analyses and one can handle a broad family nonconvex penalties. Some examples are demonstrated to show the efficacy of the proposed methodology.