Nuclear magnetic resonance (NMR) chemical shifts play a large role in the structuralcharacterization of amorphous or disordered solids. When combined with X-ray diffraction, NMR-assisted crystallography can routinely generate angstrom resolution of crystals structures. However, the solid-state NMR spectrum can be complicated and often requires chemical shift prediction models to refine and/or validate candidate structures. While density functional theory (DFT) methods provide a reasonable computational ``cost-to-accuracy'' ratio for chemical shift prediction, current methods are (1) limited in accuracy by the usage of generalized gradient approximation functionals in plane wave basis sets, or (2) become a computational bottleneck when applied to numerous structures. In this work, we describe our efforts to improve chemical shift prediction accuracy and computational cost. First, we examine a simple monomer correction to the de facto planewave DFT NMR method, GIPAW. We show that one can improve accuracy by refining the intramolecular contribution and incorporating a more accurate description, such as that obtained by hybrid functionals like PBE0 that include a fraction of exact Hartree-Fock exchange. However, not all systems are neatly described by periodic unit cells, such as biomolecular systems. In those cases, one can use a cluster approximation which models the atoms of interest and their neighbors with local atomic basis sets. To further reduce the computational cost, fragment methods, which decompose the system into many smaller/manageable calculations, can be used. We explore how polarizable continuum models (PCM) can be used on highly-charged fragments to better mimic the accuracy of cluster models with lower cost. Lastly, we developed machine learning (ML) methods to reduce the computational cost of ab initio calculations. We demonstrate the use of ML methods to reproduce PBE0/6-311+G(2d,p) predictions of solution-phase organic molecules through ∆-ML. We show that ∆-ML “corrects'' an inexpensive calculation and is 2-3 orders of magnitude faster than legacy calculations without sacrificing accuracy. Finally, we investigate a new class of ML models called graph neural networks for solid-state NMR predictions. We use convolutional and attentional graph operators for chemical shift prediction, and show the best accuracy for 15 N and 17 O compared to literature precedents.