Adaptive cross-layer designs exploit channel state information (CSI) to optimize wireless networks operating over fading channels. Capitalizing on convex optimization, duality theory and stochastic approximation tools, this paper develops channel-adaptive algorithms to allocate resources at the transport, network, link, and physical layers. Optimality here refers to maximizing a sum-utility of the average end-to-end rates, while at the same time minimizing a sum-cost of the average transmit power. Focus is placed on interference-limited access with nodes transmitting orthogonally over a set of parallel channels. The novel optimal resource allocation schemes depend on two variables: the optimum Lagrange multipliers and the available CSI. Two strategies to find the optimum value of the multipliers are investigated. The first one relies on dual gradient iterations and requires knowledge of the channel distribution. The second one relies on stochastic approximation tools, acquires the channel distribution on-the-fly, and exhibits tracking capabilities. Convergence is asserted for both strategies. Interestingly, it is shown analytically that when layers share the proper information, designs implementing a layered strategy, where each layer uses the available CSI to adapt resources separately, can be rendered optimal.