Structure elucidation is a stage of paramount importance in the discovery of novel compounds because molecular structure determines their physical, chemical and biological properties. Computational prediction of spectroscopic data, mainly NMR, has become a widely used tool to help in such tasks due to its increasing easiness and reliability. However, despite the continuous increment in CPU calculation power, classical quantum mechanics simulations still require a lot of effort. Accordingly, simulations of large or conformationally complex molecules are impractical. In this context, a growing number of research groups have explored the capabilities of machine learning (ML) algorithms in computational NMR prediction. In parallel, important advances have been made in the development of machine learning-inspired methods to correlate the experimental and calculated NMR data to facilitate the structural elucidation process. Here, we have selected some essential papers to review this research area and propose conclusions and future perspectives for the field.