Loewner's theory provides a one-to-one correspondence between Loewner chains (which is a certain family of compact sets in the complex plane) and its driver (which is a real valued continuous function). When the driver is chosen to be Brownian motion, it gives rise to Schramm-Loewner-Evolution (SLE). We will address the question: When is this family of compact sets generated by a curve? Answering this question is of fundamental importance in order to make sense of SLEs as curves. Furthermore, it also leads to other applications in SLE theory, e.g. stability with respect to perturbations in the driver.