Large fields were introduced by Florian Pop in the 1990's and have played an important role in Galois theory. Examples of large fields are pseudo algebraically closed fields, fields which are complete with respect to absolute values and more generally fraction fields of Henselian domains. In joint work with David Harbater, Julia Hartmann and Florian Pop, we solve the inverse differential Galois problem over k(x) where k is a large field of infinite transcendence degree. The first part of my talk will be about large fields and then I will explain what differential Galois theory is before I present the result mentioned above.