In this article, we survey machine repair problems (MRP) with an emphasis on historical developments of queuing models of practical importance. The survey proceeds historically, starting with developments in 1985, when the first published review on machine interference models appeared. We attempt to elaborate some basic MRP models of the real life congestion situations. The brief survey of some notable contributions done in the area of machining system has been provided. Many concepts have been incorporated while discussing the machine repair problems under consideration. The purpose of this article is to expose queuing theorists and applied probability analysts to the real time problems that arise in machine repair modeling. This survey may also be useful for machine repair modeling to the practitioners as well as to the researchers.