In this thesis we investigate the rapid release of energy in the solar corona, with a particular view to understanding the solar flare in which magnetic reconnection is thought to play a key role. A review of existing reconnection solutions is given in Chapters 2 and 3, with new analytic and numeric results are presented in subsequent chapters. Although much of the work in this thesis is computational, numerical investigations are always motivated theoretically. In Chapters 4 and 5 several aspects of two dimensional reconnection are investigated using a periodic time-dependent incompressible code. One of the main points is to check the veracity of the analytic solution of Craig and Henton (1995) by running the code from general initial conditions. Other aspects of 2-D merging covered include the tearing mode instability, osculation and the effects of finite compressibility. We employ a 3-D time-dependent code, in Chapter 4, to check that the analytically predicted spine and fan forms develop from general initial conditions. Scalings with resistivity of the associated current structures are also investigated. Most of the analytic work so far has revolved around single null magnetic configurations. Chapter 6 focuses on reconnection solutions in the presence of multiple nulls. Finally, we look at an application of the analytic theory in the context of particle acceleration. In Chapter 7 we trace proton orbits using a physically plausible analytic current sheet solution.