The first full protocol for nuclear magnetic resonance (NMR) crystallography (NMRX) using chemical shifts was developed a decade ago, and it combines experimental isotropic chemical shifts with crystal structure prediction (CSP) and with the calculation of NMR parameters. In a nutshell, a set of candidate crystal structures is generated using CSP, and then the crystal structure is determined by assessing the agreement between experimental and calculated chemical shifts (usually 1H). While this method has proven to be very powerful for structure validation and de novo crystal structure determination, it has some severe limitations. The main drawbacks of this protocol, which often prevent the application of NMRX to large and/or complex molecules, are: (i) the poor resolution of 1H solid-state NMR spectra due to the strong homonuclear dipolar coupling networks, and (ii) the computational costs of the chemical shift calculations and of the CSP protocol. This thesis focuses on the development of methods to overcome these limitations. The resolution of 1H solid-state NMR spectra can be improved either by using homonuclear dipolar decoupling sequences or by magic angle spinning (MAS). In the frame of homonuclear dipolar decoupling sequences, we make a broad comparison of the experimental performance of eight schemes developed in the past five decades, and then we provide simple guidelines for the optimization of these experiments. We also probe the limits on resolution using this approach by measuring transverse dephasing times under homonuclear decoupling. We find that coherence lifetimes are limited by the appearance of a coherent oscillatory behaviour that leads to a residual anisotropic splitting, and that this oscillation can be completely removed in a double spin-echo experiment. In the context of ultra-fast MAS, we work on the development of methods to improve 1H spectral resolution at sample spinning frequencies higher than 100.0 kHz. We first develop a method which makes use of a constant-time acquisition to remove the spectral broadening due to non-refocusable interactions. Then, assuming that part of the residual homonuclear dipolar coupling behaves like the scalar coupling in this spinning regime, we show that the anti-z-COSY pulse sequence reduces the residual line broadening of 1H NMR spectra of powdered organic solids. These methods provide up to 50% improvement in resolution compared to conventional echo experiments. To reduce the computational costs of chemical shift calculations, we develop a machine learning model to predict chemical shifts in molecular solids. This model predicts chemical shifts thousands of times faster than traditional DFT methods, while maintaining similar accuracy. We show that this method can be used as an alternative to GIPAW-DFT in NMR crystallography. Finally, we propose a modification of the current NMR crystallography protocol. We first develop a method to select the conformers in the first step of the CSP protocol based on structural constraints extracted from NMR experiments. This reduces the number of conformers selected while ensuring that the correct conformer is not excluded. Then, we introduce a Bayesian framework to determine the confidence in the identification of the crystal structure, as well as a visualization approach for the similarity between candidates in terms of their chemical shifts and of their structures to critically assess the reliability of the structure determinations.