Recent advancements in computing technology have increased the complexity of computational systems and their ability to solve larger and more complex scientific problems. Scientific applications express solutions to complex scientific problems, which often are data-parallel and contain large loops. The execution of such applications in parallel and distributed computing (PDC) environments is computationally intensive and exhibits an irregular behavior, in general due to variations of algorithmic and systemic nature. A parallel and distributed system has a set of defined policies for the use of its computational resources. Distribution of input data onto the PDC resources is dependent on these defined policies. To reduce the overall performance degradation, mapping applications tasks onto PDC resources requires parallelism detection in the application, partitioning of the problem into tasks, distribution of tasks onto parallel and distributed processing resources, and scheduling the task execution on the allocated resources. Most scheduling policies include provisions for minimizing communication among application tasks, minimizing load imbalance, and maximizing fault tolerance. Often these techniques minimize idle time, overloading resources with jobs and control overheads. Over the years, a number of scheduling techniques have been developed and exploited to address the challenges in parallel and distributed computing. In addition, these scheduling algorithms have been classified based on a taxonomy for an understanding and comparison of the different schemes. These techniques have broadly been classified into static and dynamic techniques. The static techniques are helpful in minimizing the individual task’s response time and do not have an overhead for information gathering. However, they require prior knowledge of the system and they cannot address unpredictable changes during runtime. On the other hand, the dynamic techniques have been developed to address unpredictable changes, and maximize resource utilization at the cost of information gathering overhead. Furthermore, the scheduling algorithms have also been characterized as optimal or sub-optimal, cooperative or non-cooperative, and approximate or heuristic. This chapter provides content on scheduling in parallel and distributed computing, and a taxonomy of existing (early and recent) scheduling methodologies.