The effect of an electric field on the dynamics of a fluid interface has been a subject of intense study for many years. Today applied electric fields are an important tool used to manipulate fluid interfaces on the microscale. This talk will focus on how an electric field impacts the dynamics of two complex interfaces where the effect of the electric field is less well known. First we will focus on lipid bilayer membranes which are central to our understanding of cellular membranes. The interface will be modeled as a capacitive membrane under an electric field separated by two leaky dielectric fluids. The next problem we will consider is a droplet covered with colloidal particles. Recent experiments have shown intriguing surface patterns when an electric field is applied to the droplet. The models of each case will be discussed along with analytical and computational solutions.