Elder, HenryLight that carries orbital angular momentum (OAM), also referred to as optical vortices or twisted light, is characterized by a helical or twisted wavefront ∝exp[imφ]. In contrast to spin angular momentum (SAM), where photons are limited to two states, OAM allows for, in principle, an infinite set of spatially orthogonal states. OAM-carrying light has found applications ranging from quantum key distribution in free space and guided-wave communication systems, particle trapping and optical tweezers, nanoscopy, and remote sensing. Understanding how OAM light propagates through complex environments, and how to efficiently generate particular OAM states, is critical for any such application. In the first part of this dissertation, we describe how OAM light propagates through a turbulent atmosphere. We build analytic models which describe (1) the OAM mode mixing caused by turbulence, (2) the evolution of short, high-power OAM pulses undergoing the effects of self-phase modulation (SPM) and group velocity dispersion (GVD), and (3) the evolution of high-power Gaussian pulses including SPM, GVD, and turbulence. The models are validated against both experimental data and nonlinear, turbulent pulse propagation simulation programs, the latter of which we have made freely available. We also explore how self-focusing can minimize certain deleterious effects of turbulence for OAM light. The second part of this dissertation considers nonlinear effects of OAM light propagating in azimuthally symmetric waveguides. Such waveguides have so-called spin-orbit (SO) modes, which are quantized based on their total angular momentum (TAM). We develop a generalized theory of four wave mixing-based parametric amplification of SO modes and show that these processes conserve TAM, but under certain circumstances can be taken to conserve SAM and OAM independently. Our theory is validated against a nonlinear multimode beam propagation simulation program which we developed and, again, have made freely available.enDissertationPhysicsAngular MomentumFour Wave MixingKerrNonlinear OpticsOrbital Angular MomentumTurbulence