The paper explores the potential of weighted best-first search schemes as anytime optimization algorithms for solving graphical models tasks such as MPE (Most Probable Explanation) or MAP (Maximum a Posteriori) and WCSP (Weighted Constraint Satisfaction Problem). While such schemes were widely investigated for path-finding tasks, their application for graphical models was largely ignored, possibly due to their memory requirements. Compared to the depth-first branch and bound, which has long been the algorithm of choice for optimization in graphical models, a valuable virtue of weighted best-first search is that they are tu-optimal, i.e. when terminated, they return a solution cost C and a weight w, such that C < w - C∗> where C∗ is the optimal cost. We report on a significant empirical evaluation, demonstrating the usefulness of weighted best-first search as approximation anytime schemes (that have suboptimality bounds) and compare against one of the best depth-first branch and bound solver to date. We also investigate the impact of different heuristic functions on the behaviour of the algorithms.