Increasing economic and environmental challenges leads to the need for changes in the chemical industry. In this context, a promising approach is utilizing flexible apparatuses and flexible plants to react to changing boundary conditions. However, the concept of flexibility in chemical engineering, which originated in manufacturing, still lacks a comprehensive organization and categorization of different types of flexibility. Thus, in this work, the origin of flexibility in manufacturing is traced, and a literature overview on flexibility in chemical engineering is provided. Based on a subsequent cluster analysis, four types of flexibility are identified and defined. Furthermore, this work enables research on flexibility to be integrated into a general and consistent definition of flexibility. The definitions are applied to examples from literature to achieve comparability. While enabling the qualitative assessment of flexibility, this work identifies open research gaps regarding the quantification of flexibility.