Building and operating safety critical systems requires making decisions about risk mitigations and their sufficiency. These decisions depend upon a safety case comprising many interrelated pieces of safety evidence and an argument linking these to a claim of adequate safety. Safety argumentation research has drawn from several other disciplines, including the law, philosophy, and artificial intelligence. But it has not yet achieved a normative theory of assurance argumentation that makes trustworthy predictions about the accuracy of safety claims. In this paper, we discuss the aims, achievements, and challenges of safety argumentation theory research and identify opportunities for future work.