Abstract: Quantum computing is an emerging paradigm that leverages quantum mechanics to solve problems difficult for classical computing. Realizing reliable quantum advantage requires not only hardware, but also a full software stack ranging from algorithms to operating systems. This paper provides a structured review of quantum computing systems and software, examining the current state and future directions of the field. We first introduce the architectures of quantum computing using superconducting and neutral atom systems as examples. At the software level, we begin by analyzing potential quantum applications, including physical simulation, optimization, and artificial intelligence. We then review current quantum programming interfaces, including software development kits (SDKs), verification, and program repair methods. Following these interfaces, this review introduces quantum compilation passes for quantum programs, such as mapping, decomposition, and noise mitigation, that transform logical algorithms into efficient, hardware-executable instructions. At the system level, we explore quantum operating system services such as scheduling, calibration, and error correction, which directly control quantum devices. Then, we present quantitative comparisons of gate count, circuit depth, and execution latency across various software-level methods. Finally, we discuss major challenges of quantum hardware and software, including high error rates, low operation speeds, and limited scalability. By integrating research across these levels, this review provides a comprehensive overview of quantum systems and software architectures, and highlights the significance of co-design between hardware and software.