Summary: We describe methods for mitigating the degradation in performance caused by high latencies in parallel and distributed networks. For example, given any ``dataflow'' type of algorithm that runs in \(T\) steps on an n-node ring with unit link delays, we show how to run the algorithm in \(O(T)\) steps on any \(n\)-node bounded-degree connected network with average link delay \(O(1)\). This is a significant improvement over prior approaches to latency hiding, which require slowdowns proportional to the maximum link delay. In the case when the network has average link delay \(d_{ave}\), our simulation runs in \(O(\sqrt{d_{ave}} T)\) steps using \(n/\sqrt{d_{ave}}\) processors, thereby preserving efficiency. We also show how to efficiently simulate an \(n \times n\) array with unit link delays using slowdown \(\widetilde O(d_{ave}^{2/3})\) on a two-dimensional array with average link delay \(d_{ave}\). Last, we present results for the case in which large local databases are involved in the computation.