Sequencing / Scheduling is an important process widely used in manufacturing, production, management, computer science and so on. Appropriate scheduling not only reduces manufacturing costs but also reduces possibilities for violating due dates. The present dissertation deals with the concept and applications of flow shop sequencing and scheduling model .The flow shop scheduling has been a very active and prolific research area since the seminal paper of Johnson (1954). The flow shop scheduling problem is a production problem where a set of n jobs have to be processed with identical flow pattern on m machines. In this memoir we have made an attempt to discussed some methods/approach used in flow shop scheduling/sequencing such as heuristic and meta heuristic approach,Longest – Processing Time (LPT) and the PALMER approaches for group flexible flow shop scheduling problems,flow shop sequencing with transportation time of jobs and parallel and unrelated parallel machine scheduling problems.In scheduling problems we must determine the order or sequence for processing a set of jobs through several machines in an optimal manner.