This paper presents a program for understanding turbulence through the lens of coherent structures. It introduces the concept of decomposing spatial velocity correlations orthogonally to identify coherent structures, a method pioneered by Lumley. This approach has been applied to various flows, including boundary layers, wakes, and jet flows, and is now being used for numerical simulations of channel flows. The Karhunen-Loève expansion, also known as proper orthogonal decomposition, is used to analyze these structures. This method is optimal for data compression and has been shown to compress turbulent data by orders of magnitude. The paper discusses the significance of coherent structures in the dynamical description of turbulence, suggesting that chaotic, dissipative systems may eventually be drawn into a low-dimensional strange attractor. Fluid experiments support this view, and theoretical estimates also align with this idea, though they often overestimate the attractor's dimension. The method presented here provides a practical and optimal description of the attractor by constructing an embedding space. The paper also addresses the challenge of dealing with large data sets, which has been mitigated by the availability of sufficient turbulence data. However, the method remains computationally intensive, so the paper explores the use of symmetries to extend available data and the transformation of coherent structures for use in other geometries. These transformations can change the nature of the structures but still provide useful functional bases. The paper also discusses the application of the method to various problems, including the Ginzburg-Landau equation and pattern recognition. It also reports on the successful application of the method to the Bénard problem, where it provides an accurate, low-dimensional description of turbulent convection. The paper outlines the construction of coherent structures, emphasizing the importance of incompressible flows and the boundary conditions they satisfy. It discusses the mathematical formulation of the problem, including the eigenvalue problem and the properties of the eigenfunctions. The paper also introduces the method of snapshots, which allows for the analysis of large data sets by using a reduced number of snapshots to approximate the correlation matrix. The paper concludes by discussing the implications of the method for numerical simulations, emphasizing the importance of sufficient turbulence data and the role of symmetry in reducing computational complexity. The method is shown to be effective in capturing the essential features of turbulent flows, providing a practical framework for understanding and analyzing turbulence through coherent structures.This paper presents a program for understanding turbulence through the lens of coherent structures. It introduces the concept of decomposing spatial velocity correlations orthogonally to identify coherent structures, a method pioneered by Lumley. This approach has been applied to various flows, including boundary layers, wakes, and jet flows, and is now being used for numerical simulations of channel flows. The Karhunen-Loève expansion, also known as proper orthogonal decomposition, is used to analyze these structures. This method is optimal for data compression and has been shown to compress turbulent data by orders of magnitude. The paper discusses the significance of coherent structures in the dynamical description of turbulence, suggesting that chaotic, dissipative systems may eventually be drawn into a low-dimensional strange attractor. Fluid experiments support this view, and theoretical estimates also align with this idea, though they often overestimate the attractor's dimension. The method presented here provides a practical and optimal description of the attractor by constructing an embedding space. The paper also addresses the challenge of dealing with large data sets, which has been mitigated by the availability of sufficient turbulence data. However, the method remains computationally intensive, so the paper explores the use of symmetries to extend available data and the transformation of coherent structures for use in other geometries. These transformations can change the nature of the structures but still provide useful functional bases. The paper also discusses the application of the method to various problems, including the Ginzburg-Landau equation and pattern recognition. It also reports on the successful application of the method to the Bénard problem, where it provides an accurate, low-dimensional description of turbulent convection. The paper outlines the construction of coherent structures, emphasizing the importance of incompressible flows and the boundary conditions they satisfy. It discusses the mathematical formulation of the problem, including the eigenvalue problem and the properties of the eigenfunctions. The paper also introduces the method of snapshots, which allows for the analysis of large data sets by using a reduced number of snapshots to approximate the correlation matrix. The paper concludes by discussing the implications of the method for numerical simulations, emphasizing the importance of sufficient turbulence data and the role of symmetry in reducing computational complexity. The method is shown to be effective in capturing the essential features of turbulent flows, providing a practical framework for understanding and analyzing turbulence through coherent structures.