Pure shift NMR spectroscopy, or broadband homonuclear decoupled NMR spectroscopy, produces NMR spectra that contain only chemical shift information. In a pure shift NMR spectrum the effects of J-coupling are hidden so that all multiplets are collapsed to singlets. Pure shift methods can deliver a significant improvement in resolution of NMR signals and greatly reduce signal overlap. Pure shift NMR can be achieved using direct or indirect acquisition; for direct acquisition, real-time-or interferogram-based FID collection can be used. The range of pure shift methods includes those that refocus the effects of J-coupling (BIRD, Zangger-Sterk, band selective decoupling, and anti z-COSY); manipulate the evolution of chemical shift within a constant time delay to keep the J-evolution in an indirect acquisition constant; or extract a 1-D spectrum from a 2-D J dataset. The methods and their mechanisms in weakly coupled systems are described using the product operator formalism. Examples are provided for a range of applications.