Solar flares and solar prominences are amongst the best known features of solar activity. Despite this familiarity, however, there are still significant gaps in our knowledge of these phenomena. In this thesis some theoretical aspects of these events are considered. We first consider solar prominences. We propose a model for the static equilibrium of quiescent prominences which will simultaneously explain the support mechanism for the dense prominence material and take account roughly of the required energy balance. This model contains two parameters, namely the coronal plasma beta and the horizontal shear angle Φ, that the magnetic fieldlines make with the prominence normal. We obtain limits on both these parameters which, when exceeded, imply that no equilibrium state is possible. The results obtained provide a possible explanation for several prominence features. For the remainder of the thesis we consider one aspect of the solar flare problem, namely the possibility of a trigger mechanism for the rapid release of energy in a flare. One candidate for this mechanism is the sudden release of energy stored in excess of potential by a force-free magnetic field which becomes unstable as a result of photospheric motions. For this reason we seek simple analytic solutions to the force-free field equations which may exhibit such an instability. An alternative trigger mechanism, which requires the presence of a current sheet, is given by the emerging flux model for solar flares. We thus develop a one-dimensional model for current sheets in general, where the conditions within the current sheet are given in terms of several non-dimensional parameters which describe the external conditions. These results are then applied to the emerging flux model.