Why would you want to put an index on a view?

Microsoft SQL Server allows you to add an index to a view, but why would you want to do this?

My understanding is that a view is really just a subquery, i.e., if I say SELECT * FROM myView, i'm really saying SELECT * FROM (myView's Query)

It seems like the indexes on the underlying tables would be the ones that matter the most. So why would you want a separate index on the view?