We are in the midst of a great revolution in miniaturized electronics, with nanoscale electronic elements enabling technologies such as tiny cell phones and hand-held computers. But is there a limit to how small electronics can be? In this talk, I will approach this question by discussing the past and future of a key nano-electronic element, the transistor. As transistors approach the atom-scale, their operation is limited by quantum mechanical effects. Thus, radically new technologies will be needed to overcome this fundamental physical limit. I will discuss the science and research behind some new approaches, including using novel nanomaterials and quantum computation.