The future quantum Internet (QI) will transform today's communication networks and user experiences by providing unparalleled security levels, superior quantum computational powers, along with enhanced sensing accuracy and data processing capabilities. These features will be enabled through applications like quantum key distribution (QKD) and quantum machine learning (QML). Towards enabling these applications, the QI requires the development of global quantum communication networks (QCNs) that enable the distribution of entangled resources between distant nodes. This dissertation addresses two major challenges facing QCNs, which are the scalability and coverage of their architectures, and the efficiency of their operations. Additionally, the dissertation studies the near-term deployment of QML applications over today's noisy quantum devices, essential for realizing the future QI. In doing so, the scalability and efficiency challenges facing the different QCN elements are explored, and practical noise-aware and physics-informed approaches are developed to optimize the QCN performance given heterogeneous quantum application-specific quality of service (QoS) user requirements on entanglement rate and fidelity. Towards achieving this goal, this dissertation makes a number of key contributions. First, the scaling limits of quantum repeaters is investigated, and a holistic optimization framework is proposed to optimize the geographical coverage of quantum repeater networks (QRNs), including the number of quantum repeaters, their placement and separating distances, quantum memory management, and quantum operations scheduling. Then, a novel framework is proposed to address the scalability challenge of free-space optical (FSO) quantum channels in the presence of blockages and environmental effects. Particularly, the utilization of a reconfigurable intelligent surface (RIS) in QCNs is proposed to maintain a line-of-sight (LoS) connection between quantum nodes separated by blockages, and a novel analytical model of quantum noise and end-to-end (e2e) fidelity in such QCNs is developed. The results show enhanced entangled state fidelity and entanglement distribution rates, improving user fairness by around 40% compared to benchmark approaches. The dissertation then investigates the efficiency challenges in a practical use-case of QCNs with a single quantum switch (QS). Particularly, the average quantum memory noise effects are analytically analyzed and their impacts on the allocation of entanglement generation sources and minimization of entanglement distribution delay while optimizing QS entanglement distillation operations are investigated. The results show an enhanced e2e fidelity and a minimized e2e entanglement distribution delay compared to existing approaches, and a unique capability of satisfying all users QoS requirements. This QCN architecture is scaled up with multiple QSs serving heterogeneous user requests, necessary for scalable quantum applications over the QI. Here, a novel efficient matching theory-based framework for optimizing the request-QS association in such QCNs while managing quantum memories and optimizing QS operations is proposed. Finally, after scaling QCNs and ensuring their efficient operations, the dissertation proposes novel distributed QML frameworks that can leverage both classical networks and QCNs to enable collaborative learning between today's noisy quantum devices. In particular, the first quantum federated learning (QFL) frameworks incorporating different quantum neural networks and leveraging quantum and classical data are developed, and the first publicly available federated quantum dataset is introduced. The results show enhanced performance and reductions in the communication overhead and number of training epochs needed until convergence, compared to classical counterpart frameworks. Overall, this dissertation develops robust frameworks and algorithms that advance the theoretical understanding of QCNs and offers practical insights for the future development of the QI and its applications. The dissertation concludes by analyzing some open challenges facing QCNs and proposing a vision for physics-informed QCNs, along with important future directions. / Doctor of Philosophy / In today's digital age, we are generating vast amounts of data through videos, live streams, and various online activities. This explosion of data brings not only incredible opportunities for innovation but also heightened security concerns. The current Internet infrastructure struggles to keep up with the demand for speed and security. In this regard, the quantum Internet (QI) emerges as a revolutionary technology poised to make the communication and data sharing processes faster and more secure than ever before. The QI requires the development of quantum communication networks (QCNs) that will be seamlessly integrated with today's existing communication systems that form today's Internet. This way, the QI enables ultra-secure communication and advanced computing applications that can transform various sectors, from finance to healthcare. However, building such global QCNs, requires overcoming significant challenges, including the sensitive nature and limitations of quantum devices. In this regard, the goal of this dissertation is to develop scalable and efficient QCNs that overcome the different challenges facing different QCN elements and enable a wide coverage and robust performance towards realizing the QI at a global scale. Simultaneously, machine learning (ML), which is driving significant advancements and transforming industries in today's world. Here, quantum technologies are anticipated to make a breakthrough in ML through quantum machine learning (QML) models that can handle today's large and complex data. However, quantum computers are still limited in scale and efficiency, often being noisy and unreliable. Throughout this dissertation, these limitations of QML are addressed by developing frameworks that allow multiple quantum computers to work together collaboratively in a distributed manner over classical networks and QCNs. By leveraging distributed QML, it is possible to achieve remarkable advancements in privacy and data utilization. For instance, distributed QML can enhance navigation systems by providing more accurate and secure route planning or revolutionize healthcare by enabling secure and efficient analysis of medical data. In summary, this dissertation addresses the critical challenges of building scalable and efficient QCNs to support the QI and develops distributed QML frameworks to enable near-term utilization of QML in transformative applications. By doing so, it paves the way for a future where quantum technology is integral to our daily lives, enhancing security, efficiency, and innovation across various domains.