This paper considers problems of finding non‐periodic and periodic schedules in a cycle shop which is a special case of a job shop but an extension of a flow shop. The cycle shop means the machine environment where all jobs have to pass the machines over the same route like in a flow shop but some of the machines in the route can be met more than once. We propose a classification of cycle shops and show that recently studied reentrant flow shops, robotic flow shops, loop reentrant flow shops and V shops are special cases of cycle shops. Problems solvable in polynomial time, pseudopolynomial time, NP‐hard problems and performance guarantee approximations are presented. Related earlier results are surveyed.