In most societies resources are insufficient to provide everyone with all the health care they want. In practice, this means that some people are given priority over others. On what basis should priority be given? In this paper we are interested in the general public's views on this question. We set out to synthesis what the literature has found as a whole regarding which attributes or factors the general public think should count in priority setting and what weight they should receive. A systematic review was undertaken (in August 2014) to address these questions based on empirical studies that elicited stated preferences from the general public. Sixty four studies, applying eight methods, spanning five continents met the inclusion criteria. Discrete Choice Experiment (DCE) and Person Trade-off (PTO) were the most popular standard methods for preference elicitation, but only 34% of all studies calculated distributional weights, mainly using PTO. While there is heterogeneity, results suggest the young are favoured over the old, the more severely ill are favoured over the less severely ill, and people with self-induced illness or high socioeconomic status tend to receive lower priority. In those studies that considered health gain, larger gain is universally preferred, but at a diminishing rate. Evidence from the small number of studies that explored preferences over different components of health gain suggests life extension is favoured over quality of life enhancement; however this may be reversed at the end of life. The majority of studies that investigated end of life care found weak/no support for providing a premium for such care. The review highlights considerable heterogeneity in both methods and results. Further methodological work is needed to achieve the goal of deriving robust distributional weights for use in health care priority setting.