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As technology become more advanced, those who design, use and are otherwise affected by it want to know that it will perform correctly, and understand why it does what it does, and how to use it appropriately. In essence they want to be able to trust the systems that are being designed. In this survey we present assurances that are the method by which users can understand how to trust this technology. Trust between humans and autonomy is reviewed, and the implications for the design of assurances are highlighted. A survey of research that has been performed with respect to assurances is presented, and several key ideas are extracted in order to refine the definition of assurances. Several directions for future research are identified and discussed.