Advances in insect transgenesis and our knowledge of insect physiology and genomics are making it possible to create transgenic populations of beneficial or pest insects that express novel traits. There are contexts in which we may want the transgenes responsible for these traits to spread so that all individuals within a wild population carry them, a process known as population replacement. Transgenes of interest are unlikely to confer an overall fitness benefit on those who carry them. Therefore, an essential component of any population replacement strategy is the presence of a drive mechanism that will ensure the spread of linked transgenes. We discuss contexts in which population replacement might be desirable and the requirements a drive system must satisfy to be both effective and safe. We then describe the creation of synthetic Medea elements, the first selfish genetic elements synthesized de novo, with the capability of driving population replacement, in this case in Drosophila. The strategy used to create Drosophila Medea is applicable to a number of other insect species and the Medea system satisfies key requirements for scientific and social acceptance. Finally, we highlight several challenges to implementing population replacement in the wild.