The first part of the talk will explore issues with deep networks dealing with "unknowns" inputs, and the general problems of open-set recognition in deep networks. We review the core of open-set recognition theory and its application in our first attempt at open-set deep networks, "OpenMax" We discuss is successes and limitations and why classic "open-set" approaches don't really solve the problem of deep unknowns. We then present our recent work from NIPS2018, on a new model we call the ObjectoSphere. Using ObjectoSphere loss begins to address the learning of deep features that can handle unknown inputs. We present examples of its use first on simple datasets sets (MNIST/CFAR) and then onto unpublished work applying it to the real-world problem of open-set face recognition. We discuss of the relationship between open set recognition theory and adversarial image generation, showing how our deep-feature adversarial approach, called LOTS can attack the first OpenMax solution, as well as successfully attack even open-set face recognition systems. We end with a discussion of how open set theory can be applied to improve network robustness.