The aim of this talk is to describe what we can learn about basic non-relativistic brane solutions in non-relativistic string theory from non-relativistic T-duality in the same way that relativistic T-duality has been applied in the past to relate different relativistic brane solutions. The first part of the talk will be a review of non-relativistic string theory, the equations of motion of the background fields and the T-duality symmetry. In the second part of the talk, which will be more speculative, we will discuss how we think that non-relativistic branes fit into the picture.