Abstract: This dissertation examines optical solitons---pulses or beams of light characterized by undistorted propagation---and their applications in both classical and quantum information processing. Chapter 1 includes a review of basic physical principles in soliton theory; with a treatment of both one-component scalar and two-component vector solitons, as well as an introduction to the quantum character of these nonlinear waves. It is shown that vector soliton collisions are characterized by an energy redistribution of the two component fields, making possible arbitrary computation and bistability, as explained in Chapter 3. In Chapter 4, we turn to an experimental demonstration of vector soliton propagation and collision in a birefringent optical fiber. Along with being the first demonstration of such vector solitons in the temporal (as opposed to spatial) domain, it is also the first observation of vector soliton collisions in a Kerr nonlinear medium, demonstrating the possibility for classical alloptical processing. Further study of vector solitons are discussed in Chapter 5, with a numerical investigation of multicomponent gap solitons. We show that these solitons, which arise in superposed grating structures, have useful applications in all-optical signal processing. The remainder of this Dissertation considers the quantum mechanical aspects of soliton theory and applications to quantum information processing. In Chapter 2, we introduce the quantum theory of scalar solitons, followed by an analysis of a new effect of quantum phase noise reduction in soliton collisions and its application to quantum nondemolition measurements. Subsequently, we extend the quantum theory to two-component Manakov solitons in Chapter 6, with a discussion of future work and conclusions in Chapter 7.