This thesis presents a numerical study of vortex structures in magnetized plasmas. In a first approximation, such vortices can be understood as a collection of magnetic field aligned charged filaments. Their charge distribution gives rise to slowly varying $\vbf E\times\vbf B/B^2$-drifts of the ambient plasma and the vortices embedded there. A mathematical model has been derived, studied analytically for low-dimensional vortex systems and implemented as computer code. The code has been verified by recreation of some of the analytical results.
The main focus has been on the study of macroscopic structures created by superimposing many discrete point vortex systems and on the study of homogeneous and isotropic vortex systems approximated by periodic boundary conditions. The dynamics of the structures show a wealth of phenomena for relatively simple model, including long lived coherent formations and the evolution of stable tripolar macroscopic vortex systems from the collision of two vortex pairs. Homogeneous and isotropic vortex systems display the basic properties of turbulent diffusion and transport, i.e. finite correlation time, continuous power spectra, etc. From these results we have calculated effective diffusion coefficients for a range of vortex strengths and we have found phenomenological relations between the Eulerian and Lagrangian integral time scales and mean square velocities.