A common Authentication and Authorisation Infrastructure (AAI) that would allow single sign-on to services has been identified as a key enabler for European bioinformatics. ELIXIR AAI is an ELIXIR service portfolio for authenticating researchers to ELIXIR services and assisting these services on user privileges during research usage. It relieves the scientific service providers from managing the user identities and authorisation themselves, enables the researcher to have a single set of credentials to all ELIXIR services and supports meeting the requirements imposed by the data protection laws. ELIXIR AAI was launched in late 2016 and is part of the ELIXIR Compute platform portfolio. By the end of 2017 the number of users reached 1000, while the number of relying scientific services was 36. This paper presents the requirements and design of the ELIXIR AAI and the policies related to its use, and how it can be used for serving some example services, such as document management, social media, data discovery, human data access, cloud compute and training services.