It is generally considered that reproducibility is a necessary condition for scientific results. In this talk I will discuss how the rise of computer use in research implies a principled rethinking of research processes and reporting standards. Issues include: defining what is meant by reproducible in the computational context; ensuring access to code and data used in the research; the roles of trust and reliability; and giving appropriate credit for computational contributions to science. Researchers are not alone in their efforts to address these issues. I will also outline funding agency and government responses, as well as journal and institutional efforts. Finally, I will sketch some solutions to what is being termed a "credibility crisis" regarding reproducibility.