Quantum cloud computing is an emerging paradigm that enables quantum applications and their deployment on quantum computing resources without requiring a specialized environment to host and operate physical quantum computers. This paper reviews recent advances, identifies open problems, and proposes future directions in quantum cloud computing. It discusses the state-of-the-art quantum cloud advances, including various cloud-based models, platforms, and recently developed technologies and software use cases. It also covers different aspects of quantum cloud computing, such as resource management, quantum serverless, security, and privacy problems. The paper examines open problems and proposes future directions for quantum cloud computing, including potential opportunities and ongoing research in this emerging field. Quantum computing has the potential to revolutionize many scientific fields by solving intractable computational problems beyond the capabilities of classical computers. Although quantum computers are still in the early stages of development, they have already been used to address critical problems, such as simulating the behavior of molecules and discovering new drugs. However, acquiring a dedicated physical quantum computer and hosting it is challenging due to the need for an extremely special environment. Hosting them within cloud computing environments is the most common approach, as they provide easy access to today's quantum computation resources. This model shortens the pathway to achieving quantum advantages in the current era of noisy intermediate-scale quantum (NISQ) hardware. Despite these limitations, NISQ technology offers a promising platform for exploring quantum algorithms and applications prior to the advent of fault-tolerant quantum computing. The emerging field of quantum cloud computing (QCC) combines the principles of quantum computing with cloud infrastructure, enabling remote access to quantum computers. This integration promises to significantly lower the barrier to utilizing quantum computing resources, making it feasible for researchers and developers to explore quantum algorithms without the need for their own quantum hardware. Given the rapid advancements in QCC, which democratize access to quantum computational power and facilitate a wide range of applications from cryptography to quantum machine learning and complex system simulations, there is a pressing need for a comprehensive review of the current research and developments in this area. This survey aims to examine the progress of QCC through the perspective of corresponding concepts and problems in classical cloud computing and provide a useful resource for researchers in both quantum computing and cloud computing domains. The paper organizes the key aspects of QCC into five areas: 1) computing models, 2) software use cases, 3) providers and platforms, 4) resource management, and 5) security and privacy. For each aspect, we present a summary of the pioneering work, its relationship to classical models, its variants, and its potential applications in advancing practical research. To the best of our knowledge, this is one of the first reviews of QCC, and we hope it will serve as a valuable guide for researchers and practitioners in the domain.Quantum cloud computing is an emerging paradigm that enables quantum applications and their deployment on quantum computing resources without requiring a specialized environment to host and operate physical quantum computers. This paper reviews recent advances, identifies open problems, and proposes future directions in quantum cloud computing. It discusses the state-of-the-art quantum cloud advances, including various cloud-based models, platforms, and recently developed technologies and software use cases. It also covers different aspects of quantum cloud computing, such as resource management, quantum serverless, security, and privacy problems. The paper examines open problems and proposes future directions for quantum cloud computing, including potential opportunities and ongoing research in this emerging field. Quantum computing has the potential to revolutionize many scientific fields by solving intractable computational problems beyond the capabilities of classical computers. Although quantum computers are still in the early stages of development, they have already been used to address critical problems, such as simulating the behavior of molecules and discovering new drugs. However, acquiring a dedicated physical quantum computer and hosting it is challenging due to the need for an extremely special environment. Hosting them within cloud computing environments is the most common approach, as they provide easy access to today's quantum computation resources. This model shortens the pathway to achieving quantum advantages in the current era of noisy intermediate-scale quantum (NISQ) hardware. Despite these limitations, NISQ technology offers a promising platform for exploring quantum algorithms and applications prior to the advent of fault-tolerant quantum computing. The emerging field of quantum cloud computing (QCC) combines the principles of quantum computing with cloud infrastructure, enabling remote access to quantum computers. This integration promises to significantly lower the barrier to utilizing quantum computing resources, making it feasible for researchers and developers to explore quantum algorithms without the need for their own quantum hardware. Given the rapid advancements in QCC, which democratize access to quantum computational power and facilitate a wide range of applications from cryptography to quantum machine learning and complex system simulations, there is a pressing need for a comprehensive review of the current research and developments in this area. This survey aims to examine the progress of QCC through the perspective of corresponding concepts and problems in classical cloud computing and provide a useful resource for researchers in both quantum computing and cloud computing domains. The paper organizes the key aspects of QCC into five areas: 1) computing models, 2) software use cases, 3) providers and platforms, 4) resource management, and 5) security and privacy. For each aspect, we present a summary of the pioneering work, its relationship to classical models, its variants, and its potential applications in advancing practical research. To the best of our knowledge, this is one of the first reviews of QCC, and we hope it will serve as a valuable guide for researchers and practitioners in the domain.