Model-driven engineering (MDE) and search-based software engineering (SBSE) are both relevant approaches to software engineering. MDE aims to raise the level of abstraction in order to cope with the complexity of software systems, while SBSE involves the application of metaheuristic search techniques to complex software engineering problems, reformulating engineering tasks as optimization problems. The purpose of this paper is to survey the relatively recent research activity lying at the interface between these two fields, an area that has come to be known as search-based model-driven engineering. We begin with an introduction to MDE, the concepts of models, of metamodels and of model transformations. We also give a brief introduction to SBSE and metaheuristics. Then, we survey the current research work centered around the combination of search-based techniques and MDE. The literature survey is accompanied by the presentation of references for further details.