Magnetic reconnection is a process responsible for the conversion of magnetic energy into plasma flows in laboratory, space, and astrophysical plasmas. A product of reconnection, magnetic islands have been observed in long current layers for various space plasmas, including the magnetopause, the magnetotail, and the solar corona. In this thesis, a statistical model is developed for the dynamics of magnetic islands in very large current layers, for which conventional plasma simulations prove inadequate. An island distribution function f characterizes islands by the flux they contain \psi and the area they enclose A. An integro-differential evolution equation for f describes their creation at small scales, growth due to quasi-steady reconnection, convection along the current sheet, and their coalescence with one another. The steady-state solution of the evolution equation predicts a distribution of islands in which the signature of island merging is an asymmetry in &psi-r phase space. A Hall MHD (magnetohydrodynamic) simulation of a very long current sheet with large numbers of magnetic islands is used to explore their dynamics, specifically their growth via two distinct mechanisms: quasi-steady reconnection and merging. The results of the simulation enable validation of the statistical model and benchmarking of its parameters. A PIC (particle-in-cell) simulation investigates how secondary islands form in guide field reconnection, revealing that they are born at electron skin depth scales not as islands from the tearing instability but as vortices from a flow instability. A database of 1,098 flux transfer events (FTEs) observed by Cluster between 2001 and 2003 compares favorably with the model's predictions, and also suggests island merging plays a significant role in the magnetopause. Consequently, the magnetopause is likely populated by many FTEs too small to be recognized by spacecraft instrumentation. The results of this research suggest that a complete theory of reconnection in large current sheets should account for the disparate separation of scales -- from the kinetic scales at which islands are produced to the macroscale objects observed in the systems in question.