Few topics in the social sciences have witnessed as dramatic an increase in scholarly attention over the past two decades as the topic of risk. In this essay we examine sociological approaches to risk in criminological research and theory. After briefly describing the concept of risk in classical and neoclassical criminology, we turn our attention to three emerging social science perspectives on risk, those associated with the scholarship on risk society, edgework, and governmentality. We examine the new directions that these emerging ``risk paradigms'' open for criminological theory and research, including new perspectives on the motivation for criminal risk-taking, the organization of policing and criminal justice systems, and public and political responses to crime. We conclude by reviewing critiques of the scholarship associated with the new risk paradigms and by suggesting promising future directions for criminological research seeking to advance these perspectives.