In joint work with Ted Chinburg and Andy Magid we address the problem of recognizing a differential Galois extension E of a differential field F from weaker information than the structure of E as a differential field. Our work includes a differential counterpart of the normal basis theorem in polynomial Galois theory and the construction of an invariant that depends on the differential Galois group of the extension. I will begin with a brief introduction to differential Galois theory and then present the results and examples.