In trying to get into the topic of moduli spaces of elliptic curves, the following question arises:
What is the state of the art in the topic right now?
Deligne and Rapoport describes how the moduli problems with level-$N$ structure each have a model over $\mathbb Z[1/N]$. This is according to Igusa. Next, in the preface to Katz and Mazur's book, some work of Drinfeld is mentioned and the book's aim is to apparently re-write the Deligne-Rapoport construction based on Drinfeld's work.
Here I am a bit confused. What does this given in addition? There is already a smooth model over $\mathbb Z[1/N]$; so what does Katz-Mazur give in addition?
Next, are there any advances in this topic after Katz-Mazur?