The review begins with an introduction to some of the various solar phenomena that may be investigated using stability theory. The geometry of the coronal magnetic field for many models is either a loop or an arcade and it is the stability properties of these structures that are investigated. The author presents a simple physical description of the basic MHD instabilities and describes the main difference between laboratory and coronal plasmas due to the presence of an extremely dense plasma at the footpoints of the coronal magnetic fieldlines. The implications of this density interface are discussed. Linear stability theory is applied to some solar situations and some non-linear simulations are discussed.