Summary: A novel method for performing spectral analysis of a fluid flow solely based on snapshot sequences from numerical simulations or experimental data is presented by P. J. Schmid [J. Fluid Mech. 656, 5–28 (2010; Zbl 1197.76091)]. Dominant frequencies and wavenumbers are extracted together with dynamic modes which represent the associated flow structures. The mathematics underlying this decomposition is related to the Koopman operator which provides a linear representation of a nonlinear dynamical system. The procedure to calculate the spectra and dynamic modes is based on Krylov subspace methods; the dynamic modes reduce to global linear eigenmodes for linearized problems or to Fourier modes for (nonlinear) periodic problems. Schmid [loc. cit.] also generalizes the analysis to the propagation of flow variables in space which produces spatial growth rates with associated dynamic modes, and an application of the decomposition to subdomains of the flow region allows the extraction of localized stability information. For finite-amplitude flows, this spectral analysis identifies relevant frequencies more effectively than global eigenvalue analysis and decouples frequency information more clearly than proper orthogonal decomposition.