This review provides a comprehensive overview of the current state-of-the-art in quantum arithmetic circuits, focusing on fundamental operations such as addition, subtraction, multiplication, division, and modular exponentiation. The paper discusses two mainstream design approaches: those based on the Clifford+T gate set and those based on the Quantum Fourier Transformation (QFT). It evaluates the efficiency of these designs using metrics such as Toffoli-Count, Toffoli-Depth, and Qubit-Count for Clifford+T-based circuits, and QFT-Count and Non-Clifford-CP-Count for QFT-based circuits. The paper also explores the applications of quantum arithmetic circuits in large-scale quantum algorithms and suggests future research directions. It covers various quantum arithmetic designs, including quantum adders, subtractors, multipliers, and dividers, and discusses their performance, implementation, and efficiency. The paper highlights the importance of quantum arithmetic circuits in quantum computing and their potential to accelerate quantum algorithms, quantum communication, and quantum cryptography. It also discusses the challenges and opportunities in the development of quantum arithmetic circuits, emphasizing the need for further research and innovation in this field.This review provides a comprehensive overview of the current state-of-the-art in quantum arithmetic circuits, focusing on fundamental operations such as addition, subtraction, multiplication, division, and modular exponentiation. The paper discusses two mainstream design approaches: those based on the Clifford+T gate set and those based on the Quantum Fourier Transformation (QFT). It evaluates the efficiency of these designs using metrics such as Toffoli-Count, Toffoli-Depth, and Qubit-Count for Clifford+T-based circuits, and QFT-Count and Non-Clifford-CP-Count for QFT-based circuits. The paper also explores the applications of quantum arithmetic circuits in large-scale quantum algorithms and suggests future research directions. It covers various quantum arithmetic designs, including quantum adders, subtractors, multipliers, and dividers, and discusses their performance, implementation, and efficiency. The paper highlights the importance of quantum arithmetic circuits in quantum computing and their potential to accelerate quantum algorithms, quantum communication, and quantum cryptography. It also discusses the challenges and opportunities in the development of quantum arithmetic circuits, emphasizing the need for further research and innovation in this field.