This comprehensive study reviews the current state of quantum arithmetic circuits, focusing on fundamental operations such as addition, subtraction, multiplication, division, and modular exponentiation. The paper aims to provide a systematic and accessible overview of the latest advancements in these circuits, which are crucial for various quantum algorithms, including Shor's algorithm. The review covers two main design approaches: Clifford+T gates and Quantum Fourier Transform (QFT). For each operation, the paper discusses the data formats (integer, fixed-point, floating-point), evaluation metrics (Toffoli-Depth, Toffoli-Count, Qubit-Count for Clifford+T; QFT-Count, Non-Clifford-CP-Count, Qubit-Count for QFT), and detailed implementations of both mainstream designs. The paper also explores the applications of these circuits in large-scale quantum algorithms and suggests future research directions. Key contributions include a detailed analysis of quantum adders, subtractors, multipliers, and dividers, highlighting recent advancements and potential improvements. The study underscores the importance of efficient quantum arithmetic circuits in advancing quantum computing technology and its practical applications.This comprehensive study reviews the current state of quantum arithmetic circuits, focusing on fundamental operations such as addition, subtraction, multiplication, division, and modular exponentiation. The paper aims to provide a systematic and accessible overview of the latest advancements in these circuits, which are crucial for various quantum algorithms, including Shor's algorithm. The review covers two main design approaches: Clifford+T gates and Quantum Fourier Transform (QFT). For each operation, the paper discusses the data formats (integer, fixed-point, floating-point), evaluation metrics (Toffoli-Depth, Toffoli-Count, Qubit-Count for Clifford+T; QFT-Count, Non-Clifford-CP-Count, Qubit-Count for QFT), and detailed implementations of both mainstream designs. The paper also explores the applications of these circuits in large-scale quantum algorithms and suggests future research directions. Key contributions include a detailed analysis of quantum adders, subtractors, multipliers, and dividers, highlighting recent advancements and potential improvements. The study underscores the importance of efficient quantum arithmetic circuits in advancing quantum computing technology and its practical applications.