This paper focuses on the static scheduling problem of allocating a directed acyclic graph (DAG) of tasks to multiprocessors to minimize the completion time. The DAG represents the parallel program, with nodes representing tasks and edges representing dependencies and communication costs. The scheduling problem is NP-complete, so researchers have developed various heuristics to find approximate solutions. The paper provides a taxonomy of scheduling algorithms, categorizing them based on their assumptions about the DAG structure, task execution times, and communication costs. It discusses 27 scheduling algorithms, each explained with a description and an example. The paper also outlines novel optimization approaches and current research trends, and reviews software tools for scheduling and mapping functionalities. The goal is to provide a comprehensive overview of the field, highlighting the relative merits of different algorithms in terms of performance and time complexity.This paper focuses on the static scheduling problem of allocating a directed acyclic graph (DAG) of tasks to multiprocessors to minimize the completion time. The DAG represents the parallel program, with nodes representing tasks and edges representing dependencies and communication costs. The scheduling problem is NP-complete, so researchers have developed various heuristics to find approximate solutions. The paper provides a taxonomy of scheduling algorithms, categorizing them based on their assumptions about the DAG structure, task execution times, and communication costs. It discusses 27 scheduling algorithms, each explained with a description and an example. The paper also outlines novel optimization approaches and current research trends, and reviews software tools for scheduling and mapping functionalities. The goal is to provide a comprehensive overview of the field, highlighting the relative merits of different algorithms in terms of performance and time complexity.