Multidimensional indices are becoming increasingly important instruments to assess the well-being of societies. They move beyond the focus on a single indicator and yet, are easy to present and communicate. A crucial step in the construction of a multidimensional index of well-being is the selection of the relative weights for the different dimensions. The aim of this paper is to study the role of these weights and to critically survey eight different approaches to set them. We categorize the approaches in three classes: data-driven, normative and hybrid weighting, and compare their respective advantages and drawbacks.