This paper discusses Tangible User Interfaces (TUIs) and their potential impact on cognitive assessment and cognitive training. We believe that TUIs, and particularly a subset that we dub spatial TUIs, can extend human computer interaction beyond some of its current limitations. Spatial TUIs exploit human innate spatial and tactile ability in an intuitive and direct manner, affording interaction paradigms that are practically impossible using current interface technology. As proof-of-concept we examine implementations in the field of cognitive assessment and training. In this paper we use Cognitive Cubes, a novel TUI we developed, as an applied test bed for our beliefs, presenting promising experimental results for cognitive assessment of spatial ability, and possibly for training purposes.