Layered multicast exploits the heterogeneity of user capacities, making it ideal for delivering content such as media streams over the Internet. In order to maximize either its revenue or the total utility of users, content providers employing layered multicast need to carefully choose a routing, layer allocation and pricing scheme. We study algorithms and mechanisms for achieving either goal from a theoretical perspective. When the goal is maximizing social welfare, we prove that the problem is NP-hard, and provide a simple 3-approximation algorithm. We next tailor a payment scheme based on the idea of critical bids to derive a truthful mechanism that achieves a constant fraction of the optimal social welfare. When the goal is revenue maximization, we first design an algorithm that computes the revenue-maximizing layer pricing scheme, assuming truthful valuation reports. This algorithm, coupled with a new revenue extraction procedure for layered multicast, is used to design a randomized, strategyproof auction that elicits truthful reports. Employing discrete martingales to model the auction, we show that a constant fraction of the optimal revenue can be guaranteed with high probability. Finally, we study the efficacy of our algorithms via simulations.