If both the external and the internal world turn out to be less solid than we initially thought, one thing we can still hold on to is the certainty that something is real, even if the external world is not, and even if we and our internal world are not. This, of course, is the belief in the existence of an ultimate foundation that grounds all existence. This chapter considers a series of challenges to this idea. It begins by evaluating possible arguments for the existence of such a foundation, and then describes attempts to establish its opposite, a non-foundational view of reality, also considering what role this non-foundational view plays in particular sciences, such as mathematics, physics, and cognitive science.