Covariance NMR: Theoretical concerns, practical considerations, contemporary applications and related techniques

[Display omitted] •Covariance NMR treats spectra as matrices subject to standard algebraic operations.•Covariance techniques enhance resolution and/or sensitivity of NMR spectra.•Covariance can reconstruct spectra for which experimental acquisition is infeasible.•Covariance applies to pure shift, solid state and non-uniformly sampled experiments.•Applications include protein NMR, metabolomics and process analytical technology. The family of resolution enhancement and spectral reconstruction techniques collectively known as covariance NMR continues to expand, along with the list of applications for these techniques. Recent advances in covariance NMR include the utilization of covariance to reconstruct pure shift NMR spectra, and the growing use of covariance NMR in processing non-uniformly sampled data, especially in solid state NMR and metabolomics. This review describes theoretical and practical considerations for direct and indirect covariance NMR techniques, and summarizes recent additions to the covariance NMR family. The review also outlines some of the applications of covariance NMR, and places covariance NMR in the larger context of methods that use statistical and algebraic approaches to enhance and combine various kinds of spectroscopic data, including tensor-based approaches for multidimensional NMR and heterocovariance spectroscopy.