Autonomous Parking Systems (APSs) are rapidly evolving, promising enhanced convenience, safety, and efficiency. This review critically examines the current strategies in perception, path planning, and vehicle control, alongside system-level aspects like integration, validation, and security. While significant progress has been made, particularly with the advent of deep learning and sophisticated sensor fusion, formidable challenges persist. This paper delves into the inherent trade-offs, such as balancing computational cost with real-time performance demands; unresolved foundational issues, including the verification of non-deterministic AI components; and the profound difficulty of ensuring robust real-world deployment across diverse and unpredictable conditions, ranging from cluttered urban canyons to poorly lit, ambiguously marked parking structures. We also explore the limitations of current technologies, the complexities of safety assurance in dynamic environments, the pervasive impact of cost considerations on system capabilities, and the critical, often underestimated, need for genuine user trust. Future research must address not only these technological gaps with innovative solutions but also the intricate socio-technical dimensions to realize the full potential of APS.