Transformations are a central organizing idea in geometry. They are included in most geometry curricula and are likely to appear with even greater emphasis in the future, given the central role they play in the "Common Core State Standards" for K-12 mathematics. One of the attractions of geometry is the ability to draw and construct the geometrical figures that one is studying. This opens doors to all sorts of measuring and investigating that can lead to understanding. But transformations are more elusive, since they cannot really be pictured in the same unambiguous way. It is true that visual clues made of arrows and other indicators can help one visualize a transformation. And it is also possible to get hands-on access to some properties of transformations with paper folding or mirrors. But nonetheless, key theorems and properties of transformations can be challenging to understand because of their abstraction and the difficulty of gaining intuition about them. Dynamic geometry software is one tool that provides a direct way to interact with transformations. In this article, the author suggests some "serious play" with transformations that may open doors to better understanding of difficult concepts. (Contains 14 figures.)