Deployment Scenarios for Office 365 and AAD Identity

In my previous post from yesterday on understanding Office 365 and AAD federated identity types, I talked about the two methods for allowing our users to sign in to the Microsoft cloud services with our on-premises identity using either DirSync, AADSync or FIM for same sign-on or using ADFS for single sign-on. Now that we understand the products at a high-level, I want to cover off some options for deployment scenarios and specifically, how we can leverage Microsoft Azure to host these services.