Decision-making under uncertainty is a major challenge in logistics. Mathematical optimization has a long tradition in providing powerful methods for solving logistics problems. While classical optimization models for uncertainty in the input data do not consider the option to actively query the precise value of uncertain input elements, this option is in practice often available at a certain cost. The recent line of research on optimization under explorable uncertainty develops methods with provable performance guarantees for such scenarios. In this chapter, we highlight some recent results from the mathematical optimization perspective and outline the potential power of such model and techniques for solving logistics problems.