NMR spectroscopy is one of the most powerful sources of data for elucidating molecular connectivity, conformation and dynamics. However, owing to the relative insensitivity of NMR experiments, many of the most powerful NMR techniques require intractably long measurement times to acquire sufficient data to establish molecular structure and/or shape. Covariance NMR comprises a family of techniques that use the properties of matrix algebra to re-transform NMR spectra. Direct covariance NMR leverages the inherent symmetry present in many NMR spectra to provide up to 40-fold resolution enhancements for 2D and even 4D experiments. Generalized Indirect Covariance (GIC) and Unsymmetrical Indirect Covariance (UIC) reconstruct datasets that correlate heavy atom nuclei such as 13C and 15N or 31P. Such datasets are particularly valuable as they directly represent molecular connectivity. However, at natural abundance, experimental establishment of correlations between relatively NMR-insensitive heavy atoms can take weeks. UIC and GIC, in a manner analogous and complementary to Computer Assisted Structure Elucidation (CASE) techniques, can statistically establish such correlations from experiments taking a few hours at most in some cases. Thus, covariance NMR techniques facilitate the rapid acquisition of high-resolution, high-sensitivity NMR data. Covariance NMR techniques also provide investigators with the ability to examine NMR data in a manner analogous to CASE programs, which may facilitate structure elucidation efforts.