Quantifying the relative performance of individual scholars, groups of scholars, departments, institutions, provinces/states/regions and countries has become an integral part of decision-making over research policy, funding allocations, awarding of grants, faculty hirings, and claims for promotion and tenure. Bibliometric indices (based mainly upon citation counts), such as the h-index and the journal impact factor, are heavily relied upon in such assessments. There is a growing consensus, and a deep concern, that these indices — more-and-more often used as a replacement for the informed judgement of peers — are misunderstood and are, therefore, often misinterpreted and misused. The articles in this ESEP Theme Section present a range of perspectives on these issues. Alternative approaches, tools and metrics that will hopefully lead to a more balanced role for these instruments are presented.