This article presents a comprehensive survey of research related to the Machine Interference Problem (MIP), also known as the Machine Repair Problem (MRP). The problem arises when machines fail randomly in manufacturing or service environments and compete for limited repair facilities, causing queues and production delays. Such failures often result in substantial losses of production, revenue, or reliability. In addition to summarising research articles on MIP/MRP, this paper provides an organised list of books and survey papers to aid researchers in understanding the breadth of work in the queueing domain. The literature is classified according to methodological and modelling approaches. The survey concludes by highlighting recent advances and identifying promising directions for future research in reliability and queueing theory.