Increasingly societies and their governments are facing important social issues that have science and technology as key features. A number of these socio-scientific issues have two features that distinguish them from the restricted contexts in which school science has traditionally been presented. Some of their science is uncertain and scientific knowledge is not the only knowledge involved. As a result, the concepts of uncertainty, risk and complexity become essential aspects of the science underlying these issues. In this chapter we discuss the nature and role of these concepts in the public understanding of science and consider their links with school science. We argue that these same concepts and their role in contemporary scientific knowledge need to be addressed in school science curricula. The new features for content, pedagogy and assessment of this urgent challenge for science educators are outlined. These will be essential if the goal of science education for citizenship is to be achieved with our students, who will increasingly be required to make personal and collective decisions on issues involving science and technology.