Distributed algorithmic mechanism design (DAMD) is an approach to designing distributed systems that takes into account both the distributed-computational environment and the incentives of autonomous agents. In this dissertation, we study two problems, multicast cost sharing and interdomain routing. We also touch upon several issues important to DAMD in general, including approximation, compatibility with existing protocols, and hardness that results from the interplay of incentives and distributed computation. The multicast cost-sharing problem involves choosing a set of receivers for a multicast transmission and determining payments for them to offset the bandwidth costs of the multicast. We focus on cost-sharing mechanisms that are group-strategyproof and budget-balanced. We prove fundamental lower bounds on the network complexity of group-strategyproof mechanisms that are exactly or approximately budget-balanced. The Shapley-value mechanism (SH) is perhaps the most economically compelling mechanism in this class. We give a group-strategyproof mechanism that exhibits a tradeoff between the other properties of SH: It can be computed by an algorithm that is more communication-efficient than SH, but it might fail to achieve exact budget balance or exact minimum welfare loss (albeit by a bounded amount). We also show that no strategyproof mechanism for multicast cost sharing can be both approximately efficient and approximately budget-balanced. Interdomain routing is the routing of traffic between Internet domains or Autonomous Systems, a task currently performed by the Border Gateway Protocol (BGP). We first show that there is a unique strategyproof mechanism for lowest-cost routing. Moreover, the prices required by this mechanism can be computed with a straightforward change to BGP that causes only modest increases in routing-table size and convergence time. We also formulate the policy routing mechanism-design problem. We show that, with arbitrary route valuations, it is NP-hard to find a welfare-maximizing (or even approximately welfare-maximizing) set of routes. For an important class of restricted valuations, next-hop preferences, a welfare-maximizing set of routes can be computed with a strategyproof mechanism in polynomial time (in a centralized computational model). However, we show that this mechanism appears to be incompatible with BGP, and hence is hard to compute in the context of the current Internet.