This article introduces the November 2004 issue of MRS Bulletin on the state of the art in solid-state memory and storage technologies.The memory business drives hundreds of billions of dollars in sales of electronic equipment per year. The incentive for continuing on the historical track outlined by Moore's law is huge, and this challenge is driving considerable investment from governments around the world as well as in private industry and universities. The problem is this: recognizing that current approaches to semiconductor-based memory are limited, what new technologies can be introduced to continue or even accelerate the pace of complexity? The articles in this issue highlight several commercially available memories, as well as memory technologies that are still in the research and development stages. What will become apparent to the reader is the huge diversity of approaches to this problem.