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Solid-state nuclear magnetic resonance (SSNMR) is a powerful tool for the study of chemical structure and dynamics. The interactions that manifest in NMR spectra are anisotropic (i.e., orientation dependent) in origin, often resulting in inhomogeneous broadening that can yield spectra exceeding ca. 250 kHz in breadth; such spectra are often referred to as ultra-wideline (UW) NMR spectra. In many cases, UWNMR spectra cannot be acquired using conventional methods and rectangular radiofrequency (RF) pulses – rather, specialized pulses and techniques must be implemented. Furthermore, the large suite of high-resolution methods based on magic-angle spinning (MAS) are generally unsuitable for the acquisition of UWNMR spectra. Frequency-swept (FS) pulses are amplitude- and phase-modulated pulses that can irradiate NMR frequencies over large bandwidths. One of these is the wideband uniform-rate smooth-truncation (WURST) pulse, which features a linear effective frequency sweep. WURST pulses are used in the WURST-Carr-Purcell/Meiboom-Gill (WURST-CPMG) and broadband adiabatic inversion-cross polarization (BRAIN-CP) pulse sequences, which have been shown to be effective for the acquisition of UWNMR spectra of stationary (static) samples. These sequences have limitations, and to date, their capabilities have not been fully explored, nor have they been described from a theoretical point of view in a comprehensive manner. Signal processing is an integral component of pulsed-Fourier transform NMR spectroscopy, and comprises many protocols for enhancing spectral sensitivity and resolution. There has been much interest in advanced spectral processing methods such as alternate basis transformations (i.e., besides Fourier encoding), statistical analyses (e.g., singular value decomposition, SVD, and principal component analysis, PCA), numerical regression (e.g., non-negative least squares), and the use of deep learning and neural networks. Such methodologies are now routinely implemented in imaging and multidimensional solution NMR, but are seldom explored in SSNMR. This thesis describes the development of new methods for the acquisition and advanced processing of conventional, wideline, and UW SSNMR spectra, including: (i) the design of new pulses and pulse sequences with optimal control theory (OCT); (ii) the modification of existing pulse sequences for UWNMR under MAS conditions; (iii) achieving signal enhancements with CPMG pulse sequences via the suppression of weak homonuclear dipolar coupling interactions under static and MAS conditions; (iv) the application of the BRAIN-CP pulse sequence to integer-spin nuclei, along with a thorough theoretical treatment; (v) rapid and robust measurements of longitudinal relaxation time constants (T1) and T1 anisotropies from UWNMR spectra under static conditions; (vi) the development and application of advanced processing methods for resolving UWNMR relaxation data with inverse Laplace transforms; and (vii) the development of a Python library for denoising 1D and 2D NMR spectra with SVD, PCA, and wavelet transforms. It is hoped that these methods will open up the Periodic Table of elements to increasingly routine exploration by SSNMR spectroscopy, aiding researchers in chemistry, biochemistry, materials science, and physics with advanced molecular-level characterization of their materials.