Electrostatic fiber formation, also known as "electrospinning", has emerged in recent years as the popular choice for producing continuous threads, fiber arrays and nonwoven fabrics with fiber diameters below 1 microm for a wide range of materials, from biopolymers to ceramics. It benefits from ease of implementation and generality of use. Here, we review some of the basic aspects of the electrospinning process, as it is widely practiced in academic laboratories. For purposes of organization, the process is decomposed into five operational components: fluid charging, formation of the cone-jet, thinning of the steady jet, onset and growth of jet instabilities that give rise to diameter reduction into the submicron regime, and collection of the fibers into useful forms. Dependence of the jetting phenomenon on operating variables is discussed. Continuum level models of the jet thinning and jet instability are also summarized and put in some context.