Synthetic biology is an emerging field at the interface between biology and engineering, which has generated many expectations for beneficial biomedical and biotechnological applications. At the same time, however, it has also raised concerns about risks or the aim of producing new forms of living organisms. Researchers from different disciplines as well as policymakers and the general public have expressed the need for a form of technology assessment that not only deals with technical aspects, but also includes societal and ethical issues. A recent and very influential model of technology assessment that tries to implement these aims is known as RRI (Responsible Research and Innovation). In this paper, we introduce this model and its historical precursor strategies. Based on the societal and ethical issues which are presented in the current literature, we discuss challenges and opportunities of applying the RRI model for the assessment of synthetic biology.