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One definition of the word “distributed system” describes it as “a set of entities that collaborate in order to find a solution to a problem that cannot be solved by a single entity using their own resources.” This description of a distributed system is an example of a distributed system. As the number of algorithms that are mathematically complicated continues to increase, distributed computing systems have emerged as a direct result of this trend. The optimization of a distributed computing system has been accomplished via the development of methods for the distribution of work and the scheduling of jobs. Because of this, the system has been able to be used in a more efficient manner. Task scheduling refers to the process of selecting the order in which actions are carried out in response to a given set of circumstances. On the other hand, task allocation is the process of allocating tasks to the processors in a system that are the most fit for taking on those tasks. This procedure determines which processors are assigned the jobs. Within the context of distributed systems, the objective of this article is to provide a detailed review of the several approaches to task scheduling that have been used by researchers.