The ability to move production between different geographical locations has recently become more important, due to the increasing need for sustainability and faster response times, complying with local regulations, and dealing with brittle international supply chains. To this end, the movable factory concept has been put forward, which is defined as mobile production units that can be installed near the customer's location. Unfortunately, industrial paradigms such as Industry 4.0 make little if any notice of movable factories but instead focus on the digitalization of their fixed counterparts. In the form of a systematic literature review, this paper breaks down the concept of the movable factory, relates it to the state-of-the-art, and summarizes its main use cases, requirements, research gaps, and opportunities. The review covers over 100 relevant articles published in the past two decades. Compared to existing surveys, we have not only focused on the motivations for movable factories, but also identified research gaps and discuss the impact of modern technologies such as Internet-of-Things, digital twins, and modeling and simulation in fulfilling these gaps. The result is a survey of the state-of-the-art and a list of domains for potential future research on different aspects of movable factories.