Algorithmic decision systems have frequently been labelled as "biased", "racist", "sexist", or "unfair" by numerous media outlets, organisations, and researchers. There is an ongoing debate about whether such assessments are justified and whether citizens and policymakers should be concerned. These and other related matters have recently become a hot topic in the context of biometric technologies, which are ubiquitous in personal, commercial, and governmental applications. Biometrics represent an essential component of many surveillance, access control, and operational identity management systems, thus directly or indirectly affecting billions of people all around the world. Recently, the European Association for Biometrics organised an event series with "demographic fairness in biometric systems" as an overarching theme. The events featured presentations by international experts from academic, industry, and governmental organisations and facilitated interactions and discussions between the experts and the audience. Further consultation of experts was undertaken by means of a questionnaire. This work summarises opinions of experts and findings of said events on the topic of demographic fairness in biometric systems including several important aspects such as the developments of evaluation metrics and standards as well as related issues, e.g. the need for transparency and explainability in biometric systems or legal and ethical issues.