Quantum circuit transpilation is a critical component in the quantum computing stack, bridging the gap between abstract quantum algorithms and the physical constraints of quantum hardware. This survey provides a comprehensive overview of quantum circuit transpilation techniques from foundational methods to state-of-the-art approaches. We explore the evolution of transpilation strategies, discuss current challenges, and examine emerging trends with a particular focus on AI-driven methods and adaptations for fault-tolerant quantum computing. By synthesizing recent advancements and identifying open problems, this survey aims to provide researchers and practitioners with a roadmap for future developments in quantum circuit optimization.