Governments, universities, and companies expend vast resources building the top supercomputers. The processors and interconnect networks become faster, while the number of nodes grows exponentially. Problems of scale emerge, not least of which is collective performance. This thesis identifies and proposes solutions for two major scalability problems. Our first contribution is a novel algorithm for process-partitioning and remapping for exascale systems that has far better time and space scaling than known algorithms. Our evaluations predict an improvement of up to 60x for large exascale systems and arbitrary reduction in the large temporary buffer space required for generating new communicators. Our second contribution consists of several novel collective algorithms for Clos and torus networks. Known allgather, reduce-scatter, and composite algorithms for Clos networks suffer the worst congestion when the largest messages are exchanged, damaging performance. Known algorithms for torus networks use only one network port, regardless of how many are available.