Supply chain planning is based on the assumption of fixed production locations. This appears justified insofar as location decisions are usually strategic in nature and, traditionally, cannot be revised in the short term. Due to the development of new technologies and modularization in recent years, a completely new situation has emerged with the consideration of mobile and modular units whose locations can be changed in a short amount of time at a comparatively low cost. This has sparked interest in studying the (re)positioning of more-flexible networks. Therefore, we review and classify 125 contributions addressing the location problem with mobile and modular facilities. We provide a broad overview of their mathematical formulations, solution approaches, objectives, and main characteristics. Finally, we categorize case studies that have been presented in the literature and identify research trends for further developments in this field.