This tutorial paper reviews recent advancements in optimization-based approaches for resource allocation in wireless systems, focusing on opportunistic scheduling in cellular networks and multi-hop wireless networks. It begins by discussing the effectiveness of myopic policies in cellular networks, where channel-aware scheduling optimizes system performance. The paper then addresses the challenges of extending these methods to multi-hop networks, highlighting the need for a "loosely coupled" cross-layer solution. This solution involves algorithms that map to different layers (transport, network, and MAC/PHY) with limited information exchange. The complexity of the optimal scheduling component at the MAC layer is addressed by simpler, potentially imperfect distributed solutions. The paper demonstrates how to use imperfect scheduling in the cross-layer framework and describes recent distributed algorithms. Finally, it concludes by outlining open research problems in cross-layer optimization.This tutorial paper reviews recent advancements in optimization-based approaches for resource allocation in wireless systems, focusing on opportunistic scheduling in cellular networks and multi-hop wireless networks. It begins by discussing the effectiveness of myopic policies in cellular networks, where channel-aware scheduling optimizes system performance. The paper then addresses the challenges of extending these methods to multi-hop networks, highlighting the need for a "loosely coupled" cross-layer solution. This solution involves algorithms that map to different layers (transport, network, and MAC/PHY) with limited information exchange. The complexity of the optimal scheduling component at the MAC layer is addressed by simpler, potentially imperfect distributed solutions. The paper demonstrates how to use imperfect scheduling in the cross-layer framework and describes recent distributed algorithms. Finally, it concludes by outlining open research problems in cross-layer optimization.