We are on the cusp of the emergence of a new wave of nonvolatile memory technologies that are projected to become the dominant type of main memory in the near future. A key property of these new memory technologies is their asymmetric read-write costs: Writes can be an order of magnitude or more higher energy, higher latency, and lower (per module) bandwidth than reads. This high cost for writes motivates a rethinking of algorithm design towards "write efficient" algorithms and data structures that reduce their number of writes [1, 2, 3, 4, 5, 6]. Many popular techniques for sequential, distributed, and parallel algorithms are tuned to the setting where reads and writes cost the same, and hence need to be revisited. Prior work on reducing writes to contended cache lines in shared memory algorithms can be useful here, but with the new technologies, even writes to uncontended memory is costly. Moreover, the new technologies are unlikely to replace the fastest cache memory, motivating the study of a multi-level memory hierarchy comprised of smaller symmetric level(s) and a larger asymmetric level. Lower bounds, too, need to be revisited in light of asymmetric costs. This talk provides background on these emerging memory technologies, highlights the progress to date on these exciting research questions, and touches on a few of the many open problems.