The chapter discusses the application of symmetry considerations in determining coherent structures in turbulent flows. Symmetry groups, such as translations and rotations, can significantly extend the available data and simplify the numerical or physical experiments. The author outlines the effects of these symmetries for various standard geometries, including plane Poiseuille flow, rectangular channel flow, and the Bénard problem (convection). For each geometry, the chapter explains how symmetry transformations can be used to average over admissible flows, leading to a more homogeneous and invariant correlation matrix. This averaging process increases the effective data set and simplifies the eigenfunction calculation. The chapter also explores the transformation of coherent structures under changes in flow parameters and geometry, providing methods for extending results from one geometry to others. Finally, the author discusses the implications of symmetry in error estimates and data cleanup, as well as the potential for further reduction in the formulation of the problem.The chapter discusses the application of symmetry considerations in determining coherent structures in turbulent flows. Symmetry groups, such as translations and rotations, can significantly extend the available data and simplify the numerical or physical experiments. The author outlines the effects of these symmetries for various standard geometries, including plane Poiseuille flow, rectangular channel flow, and the Bénard problem (convection). For each geometry, the chapter explains how symmetry transformations can be used to average over admissible flows, leading to a more homogeneous and invariant correlation matrix. This averaging process increases the effective data set and simplifies the eigenfunction calculation. The chapter also explores the transformation of coherent structures under changes in flow parameters and geometry, providing methods for extending results from one geometry to others. Finally, the author discusses the implications of symmetry in error estimates and data cleanup, as well as the potential for further reduction in the formulation of the problem.