As autonomous systems are becoming part of our daily lives, ensuring their trustworthiness is crucial. There are a number of techniques for demonstrating trustworthiness. Common to all these techniques is the need to articulate specifications. In this paper, we take a broad view of specification, concentrating on top-level requirements including but not limited to functionality, safety, security and other non-functional properties. The main contribution of this article is a set of high-level intellectual challenges for the autonomous systems community related to specifying for trustworthiness. We also describe unique specification challenges concerning a number of application domains for autonomous systems.