The escaping set plays an important role in the iteration of transcendental entire functions. There are many transcendental entire functions whose escaping set has a topological structure known as `a spider's web'. A spider's web is a connected set which contains `loops' that surround each other. We adapt the definition of a spider's web to the punctured plane, and study its connection with the usual spider's web in the complex plane. Finally we construct the first example of a transcendental self-map of the punctured plane whose escaping set is a spider's web. This is joint work with D. Marti-Pete and D. Sixsmith.