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This issue of SIAM Review presents “Research and Education in Computational Science and Engineering” in the Education section. This is a collaborative report, coauthored by U. Rüde, K. Willcox, L. Curfman McInnes, and H. De Sterck, surveying current challenges and future directions for computational science and engineering research and education. Twenty-nine other scientists and educators have contributed to this survey representing the views of the SIAM Activity Group on Computational Science and Engineering. The article starts with a definition of computational science and engineering (CSE) as a multidisciplinary field integrating mathematics, statistics, computer science, and core disciplines of science and engineering. Its subject is the development and use of computational methods for scientific discovery. The first part of the article makes us aware of the large impact of CSE on science, technology, and our society in general. The emergence of this new field and its advance cannot be taken for granted; it requires thoughtful design of educational programs integrating knowledge and research in interacting areas, keeping a forward view on strategically important directions. The impact of CSE is amplified by the growing presence of massive data sets and increasing computing power which enable data-driven approaches to scientific discovery. Throughout the article, the authors highlight several examples of recent success stories such as computational medicine, computer animation, CSE in the petroleum industry, climate research, and others, which demonstrate the key role of CSE theory, methods, and software in modern science and industry. The second part of the article outlines directions where new challenges appear and substantial advances would bring a qualitative leap in CSE. Mathematical models with increased robustness and stability, algorithms of better efficiency and smaller complexity, advances in nonsmooth optimization and optimal control, and uncertainty quantification for high-fidelity prediction are among the key areas discussed. Next, the report addresses the needs in education and research, the scope and specificity of educational programs which will bring forth a capable and agile workforce. The authors note that almost all sectors of industry, the national laboratories, and the government are using more sophisticated predictive models, high-end computing, and mathematical model-aided decision-making more frequently. Graduates with interdisciplinary expertise are in very high demand due to the need to develop and utilize advanced mathematical models and computational methods in their respective scientific, engineering, or business fields in order to “give the business the ability to compete and survive.” Here the authors cite statements of the National Council on Competitiveness and the U.S. Department of Energy Advanced Scientific Computing Advisory Committee. CSE educational programs have to address the growing demand for CSE professionals at both undergraduate and graduate levels, as well as provide possibilities for continuing education and professional development. Specific recommendations for the content of undergraduate programs are included in section 3.2 of the article. Substantial attention is paid to the set of learning outcomes that a CSE graduate program should target. The authors predict a growing demand for terminal master's degrees for the needs of industry and national laboratories. The education of CSE professionals should include three main components defined as follows. The graduate should possess a solid foundation in applied mathematics, including probability and statistics; should have an understanding of modern computing, computer science, programming languages, principles of software engineering, and high-performance computing; and should have good knowledge of modern science and engineering. Of course, the breadth and depth of topics covered would depend on the focus of the specific degree. The authors distinguish between the following categories in CSE preparation: CSE domain scientists and engineers preparing themselves as method users or as method developers; core researchers and developers focusing on broadly applicable methods; and scientists preparing to deal with uncertainty quantification and data science. These roles determine essential aspects of the educational programs. The report contains also a discussion on the role and interaction of two areas within CSE education: parallel extreme-scale computing and computing with massive data. The authors also elaborate on software sustainability and data management, which become more involved as software is frequently offered by geographically distributed developers. Growing concern about reproducibility of scientific results based on code and data generates additional demand for skilled professionals. Therefore, on one hand CSE education should account for these needs; on the other hand, those areas offer new research opportunities. In the final part of the third chapter, some thoughts on the changing educational infrastructure are shared: online digital materials and open educational resources including open online courses provide new ways and opportunities to enhance the learning process. The report concludes with findings and recommendations regarding the emergence of CSE, its role, and education.