This paper surveys the state of the art in deterministic sequencing and scheduling, focusing on optimization and approximation algorithms. It discusses various scheduling problems, including single machine, parallel machine, and open, flow, and job shop scheduling. The paper introduces a three-field problem classification system to categorize scheduling problems based on job data, machine environment, and optimality criteria. It covers the complexity of these problems, the algorithms used to solve them, and the results of approximation algorithms. Special cases considered include single machine scheduling, identical, uniform, and unrelated parallel machine scheduling, and open, flow, and job shop scheduling. The paper also discusses the computational complexity of these problems and the challenges in solving them. It highlights the importance of understanding the complexity of scheduling problems and the need for further research in this area. The paper provides a comprehensive overview of the current state of research in deterministic scheduling theory and its applications.This paper surveys the state of the art in deterministic sequencing and scheduling, focusing on optimization and approximation algorithms. It discusses various scheduling problems, including single machine, parallel machine, and open, flow, and job shop scheduling. The paper introduces a three-field problem classification system to categorize scheduling problems based on job data, machine environment, and optimality criteria. It covers the complexity of these problems, the algorithms used to solve them, and the results of approximation algorithms. Special cases considered include single machine scheduling, identical, uniform, and unrelated parallel machine scheduling, and open, flow, and job shop scheduling. The paper also discusses the computational complexity of these problems and the challenges in solving them. It highlights the importance of understanding the complexity of scheduling problems and the need for further research in this area. The paper provides a comprehensive overview of the current state of research in deterministic scheduling theory and its applications.