Abstract: The Borexino solar neutrino detector should begin operations in late 2006. This scintillation-based detector will observe low-energy neutrinos, in real time, down to about 250 keV. The experiment should further tighten constraints on the neutrino oscillation parameters, and confirm the Standard Solar Model of solar neutrino production. It may also observe geoneutrinos; supernova neutrinos, should the timing of the experiment be fortunate; and perhaps other processes beyond the scope of the Standard Model of particle physics. At the heart of Borexino lie 300 tons of organic scintillator fluid, contained by a spherical vessel composed of transparent nylon film. Roughly 300 tons of passive buffer fluid lie between this inner vessel and a second outer nylon vessel. Both vessels are located inside a steel sphere that also supports over 2000 inward-pointing photomultiplier tubes. The two most vital components of Borexino are these nylon vessels and the scintillator itself. Numerous measurements made at Princeton of the physical and radiochemical properties of the vessel film are reported in this thesis. A 4-ton prototype of Borexino, the CTF, has been used to study scintillator radiopurity for over ten years. However, certain peculiarities of its design make determining the spatial positions of radioactive decays within the detector difficult. The development of a new position reconstruction code that takes these problems into account is reported herein. Several studies of radiopurity in the latest version of CTF were made using this new code. These include a proposal for individually tagging decays of radon and four daughter isotopes; an attempt to detect convection using the radon daughters; a hypothesis to explain peculiar behavior of the crucial isotope 210Po; and an analysis of 40K contamination inside the detector based on models of the spatial distribution of external γ rays, leading to a somewhat concerning result. A final distillation test of the scintillator will take place shortly, and will match as closely as possible the procedure used to purify scintillator for the full Borexino detector. Analyses run on CTF data collected after this test should prove vital in understanding the detector sensitivity of Borexino.