In this thesis, I present work spanning a variety of topics relating to neutron star lowmass X-ray binaries (LMXBs) and utilize spectral information from X-ray observations to further our understanding of these sources. First, I give an overview of important X- ray astrophysics relevant to the work I present in subsequent chapters, as well as information about the X-ray observatories from which I obtained my data. In the next three chapters, I consider spectra-both high- and low-resolution--of accretion-powered millisecond X-ray pulsars, a unique and relatively new class of objects. In addition to analysis of the pulsar XTE J1814-338, I compare a broader sample of pulsars with a sample of atoll sources in order to better understand why the latter class do not contain persistently pulsating neutron stars. In particular, I test the hypothesis that pulsations in the atoll sources are suppressed by a high-optical- depth scattering region. Using X-ray color-color diagrams to define a selection criterion based on spectral state, I analyze Rossi X-ray Timing Explorer (RXTE) spectra from all the sources, and use a Comptonization model to obtain measurements of their optical depths. I then discuss efforts to spatially resolve X-ray jets from the accretion-powered millisecond pulsar SAX J1808.4-3658 and the Z source XTE J1701-462. Each was observed by the Chandra X-ray Observatory to produce a high-spatial-resolution image. This work was motivated in part by my analysis of XTE J1814-338, which found an apparent excess of infrared flux which could be attributed to jet emission. Next, I discuss the measured temperatures of thermonuclear X-ray bursts. The detection of line features in these bursts, and hence from the surfaces of neutron stars, has been an important goal for high-resolution X-ray spectroscopy. A measurement of the wavelengths of identified line features would yield a measurement of the neutron star's gravitational redshift, which would help constrain current models for the neutron star equation of state.