Quantum compilation, critical for bridging high-level quantum programming and physical hardware, faces unique challenges distinct from classical compilation. As quantum computing advances, scalable and efficient quantum compilation methods become necessary. This paper surveys the landscape of quantum compilation, detailing the processes of qubit mapping and circuit optimization, and emphasizing the need for integration with classical computing to harness quantum advantages. Techniques such as Variational Quantum Eigensolver (VQE) exemplify hybrid approaches, highlighting the potential synergy between quantum and classical systems. It is concluded that, while quantum compilation retains many classic methodologies, it introduces novel complexities and opportunities for optimization and verification, essential for the evolving field of quantum computing.