This tutorial discusses recent developments in cross-layer optimization for wireless networks, focusing on resource allocation in cellular and multi-hop wireless systems. It begins by reviewing opportunistic scheduling in cellular networks, where myopic policies optimize system performance. It then addresses the challenges of extending these methods to multi-hop networks, highlighting the need for a "loosely coupled" cross-layer solution. The paper shows that optimal scheduling at the MAC layer is complex, necessitating simpler, distributed solutions. It describes recent distributed algorithms and open research problems. The tutorial explores two key cross-layer problems: opportunistic scheduling in cellular networks and joint congestion control and scheduling in multi-hop networks. It emphasizes the use of convex programming, Lagrange duality, and other optimization techniques to solve these problems. However, it notes that many wireless problems are non-convex, requiring advanced methods for effective solutions. The paper discusses the stability of opportunistic scheduling schemes, showing that queue-length information is critical for throughput optimization. It also addresses the limitations of such approaches and the need for joint congestion control and scheduling to ensure system stability. For multi-hop wireless networks, the tutorial presents two formulations: node-centric and link-centric. These formulations help decompose the cross-layer problem into congestion control and scheduling components. The node-centric formulation considers destination-specific constraints, while the link-centric formulation focuses on link-specific constraints. Both formulations lead to convex optimization problems, enabling efficient solutions. The paper also discusses cases where perfect scheduling is solvable, such as in cellular networks or node-exclusive interference models. It highlights the complexity of scheduling in wireless networks and the need for imperfect scheduling policies. It introduces the concept of $ S_{\gamma} $-policies, which provide suboptimal but efficient solutions. These policies ensure a certain fraction of the overall capacity region and are shown to maintain stability and fairness in dynamic environments. Finally, the tutorial reviews distributed scheduling algorithms that can be implemented in a decentralized manner. These algorithms focus on maximal policies that satisfy interference constraints and ensure system stability. The paper concludes with open research problems in cross-layer optimization for wireless networks.This tutorial discusses recent developments in cross-layer optimization for wireless networks, focusing on resource allocation in cellular and multi-hop wireless systems. It begins by reviewing opportunistic scheduling in cellular networks, where myopic policies optimize system performance. It then addresses the challenges of extending these methods to multi-hop networks, highlighting the need for a "loosely coupled" cross-layer solution. The paper shows that optimal scheduling at the MAC layer is complex, necessitating simpler, distributed solutions. It describes recent distributed algorithms and open research problems. The tutorial explores two key cross-layer problems: opportunistic scheduling in cellular networks and joint congestion control and scheduling in multi-hop networks. It emphasizes the use of convex programming, Lagrange duality, and other optimization techniques to solve these problems. However, it notes that many wireless problems are non-convex, requiring advanced methods for effective solutions. The paper discusses the stability of opportunistic scheduling schemes, showing that queue-length information is critical for throughput optimization. It also addresses the limitations of such approaches and the need for joint congestion control and scheduling to ensure system stability. For multi-hop wireless networks, the tutorial presents two formulations: node-centric and link-centric. These formulations help decompose the cross-layer problem into congestion control and scheduling components. The node-centric formulation considers destination-specific constraints, while the link-centric formulation focuses on link-specific constraints. Both formulations lead to convex optimization problems, enabling efficient solutions. The paper also discusses cases where perfect scheduling is solvable, such as in cellular networks or node-exclusive interference models. It highlights the complexity of scheduling in wireless networks and the need for imperfect scheduling policies. It introduces the concept of $ S_{\gamma} $-policies, which provide suboptimal but efficient solutions. These policies ensure a certain fraction of the overall capacity region and are shown to maintain stability and fairness in dynamic environments. Finally, the tutorial reviews distributed scheduling algorithms that can be implemented in a decentralized manner. These algorithms focus on maximal policies that satisfy interference constraints and ensure system stability. The paper concludes with open research problems in cross-layer optimization for wireless networks.