Iwasawa theory is a powerful technique for understanding the link between the special values of L-functions and arithmetic objects (such as class groups of number fields, or Mordell--Weil groups of elliptic curves). In this talk I'll discuss what Iwasawa theory predicts for the symmetric square L-function attached to a modular form; and I'll describe some recent results (joint with Sarah Zerbes) confirming some of these conjectures, using the method of Euler systems."