Power system flexibility relates to the ability of the power system to manage changes. Solutions providing advances in flexibility are of utmost importance for the future power system. Development and deployment of innovative technologies, communication and monitoring possibilities, as well as increased interaction and information exchange, are enablers to provide holistic flexibility solutions. Furthermore, development of new methods for market design and analysis, as well as methods and procedures related to system planning and operation, will be required to utilise available flexibility to provide most value to society. However, flexibility is not a unified term and is lacking a commonly accepted definition. The flexibility term is used as an umbrella covering various needs and aspects in the power system. This situation makes it highly complex to discuss flexibility in the power system and craves for differentiation to enhance clarity. In this report, the solution has been to differentiate the flexibility term on needs, and to categorise flexibility needs in four categories: Flexibility for Power, Flexibility for Energy, Flexibility for Transfer Capacity, and Flexibility for Voltage. Here, flexibility needs are considered from over-all system perspectives (stability, frequency and energy supply) and from more local perspectives (transfer capacities, voltage and power quality). With flexibility support considered for both operation and planning of the power system, it is required in a timescale from fractions of a second (e.g. stability and frequency support) to minutes and hours (e.g. thermal loadings and generation dispatch) to months and years (e.g. planning for seasonal adequacy and planning of new investments). The categorisation presented in this report supports an increased understanding of the flexibility needs, to be able to identify and select the most suitable flexibility solutions.