The advent of controllable synthetic methods for the production of semiconductor nanostructures has led to their use in a host of applications, including light-emitting diodes, field effect transistors, sensors, and even television displays. This is, in part, due to the size, shape, and morphologically dependent optical and electrical properties that make this class of materials extremely customizable; wire-, rod- and sphere-shaped nanocrystals are readily synthesized through common wet chemical methods. Most notably, confining the physical dimension of the nanostructure to a size below its Bohr radius (aB) results in quantum confinement effects that increase its optical energy gap. Not only the size, but the shape of a particle can be exploited to tailor its optical and electrical properties. For example, confined CdSe quantum dots (QDs) and nanowires (NWs) of equivalent diameter possess significantly different optical gaps. This phenomenon has been ascribed to electrostatic contributions arising from dielectric screening effects that are more pronounced in an elongated (wire-like) morphology.Semiconducting nanostructures have thus received significant attention over the past two decades. However, surprisingly little work has been done to elucidate their basic photophysics on a single particle basis. What has been done has generally been accomplished through emission-based measurements, and thus does not fully capture the full breadth of these intriguing systems. What is therefore needed then are absorption-based studies that probe the size and shape dependent evolution of nanostructure photophysics. This thesis summarizes the single particle absorption spectroscopy that we have carried out to fill this knowledge gap. Specifically, the diameter-dependent progression of one-dimensional (1D) excitonic states in CdSe NWs has been revealed. This is followed by a study that focuses on the polarization selection rules of 1D excitons within single CdSe NWs. Finally, shape effects are explored by probing the absorption spectra of CdSe nanowires and nanorods of varying length. All experimental studies are complemented by theoretical predictions from an effective mass model that takes electrostatic interactions into account. Thus, this thesis seeks to show the delicate interplay between quantum confinement and dielectric screening effects in single CdSe nanostructures.