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In this article we discuss fairness in queues, view it in the context of social justice at large, and survey the recently published research work and publications dealing with the issue of measuring fairness of queues. The emphasis is placed on the underlying principles of the different measurement approaches, on reviewing their methodology, and on examining their applicability and intuitive appeal. Some quantitative results are also presented. The article has three major parts (sections) and a short concluding discussion. In the first part we discuss fairness in queues and its importance in the broader context of the prevailing conception of social justice at large, and the distinction between fairness of the queue and fairness at large is illuminated. The second part is dedicated to explaining and discussing three main properties expected of a fairness measure: conformity to the general concept of social justice, granularity, and intuitive appeal and rationality. The third part reviews the fairness of the queue evaluating and measuring approaches proposed and studied in recent years. We describe the underlying principles of the different approaches, present some of their results, and review them in context of the three main properties expected from a measure. The short discussion that follows centers on future research issues.