One area of fundamental plasma physics which remains poorly understood is the transport of particles across magnetic field lines at rates significantly higher than predicted by theory exclusively based on collisions. This "anomalous" transport is observed in many different classes of plasma experiment. Notably, both magnetic confinement fusion devices and Hall thrusters exhibit anomalous cross-field particle diffusion. This higher than predicted "loss" of particles has significant practical implications for both classes of experiment. In the case of magnetic confinement fusion experiments, such as tokamaks, the Lawson criterion nT[tau]E >/= 1021 [keV. s. M- 3] dictates that the reactant particles in a fusion plasma must be confined for a sufficient time to fuse. Higher than predicted cross-field transport decreases the effectiveness of the magnetic confinement and makes fusion more difficult to achieve. For Hall thrusters, enhanced cross-field electron mobility reduces the efficiency of the thruster. As a result, more propellant and power is required to achieve the same thrust. The goal of this thesis is to review observed and predicted fluctuation induced particle transport in Hall thrusters and tokamaks. To date, significant work has been done within both the tokamak and propulsion communities to attempt to quantify the effect of turbulent fluctuations of plasma parameters on anomalous cross-field transport. However, our understanding of the fundamental physical processes that lead to anomalously high cross-field transport remains incomplete. These two regimes of plasma physics are very different in several important ways. The magnetic field strength and field orientation, the device size, the collisionality of different species, the ion mass, and the presence of neutrals are all areas with significant differences between tokamaks and Hall thrusters. However, there are similarities as well. For example, the edge density and temperature in a tokamak are similar to those found in Hall thrusters, both have magnetized electrons, drift waves occur in both regimes and many of the observed fluctuations are of similar scale. Generally, research on cross-field transport within the tokamak community is isolated from work done within the thruster community. However, analysis of physics within both regimes reveals a rich set of complex fluctuations across a broad frequency spectrum, which contribute to cross-field transport. By studying the relevant phenomena in tandem, we can reveal fundamental processes present in both regimes. Hopefully, this will lead to a global explanation for these elusive physical processes.