Dynamics CRM 2015 and Dynamics CRM Online 2015 now support integration with Microsoft Azure. This means that you can use Azure as a channel to communicate runtime data from Dynamics CRM for requirements such as synchronization with other CRM servers.
In more news, Microsoft has published the Azure Mobile Connector SDK to connect to Dynamics CRM Online and allow built-in sync and integration with Azure Active Directory.
Azure can fill in some of the gaps of Dynamics CRM Online, such as offloading reporting or loading CRM data into business intelligence tools. You can use Azure blob storage for document storage in order to reduce storage requirements for Dynamics CRM Online.
Azure can provide a great development platform for Dynamics CRM so you avoid the short lifespan of Online trial accounts as well as the performance demands of local virtual machines on the developer's laptop. There are step-by-step instructions by Microsoft MVP Jukka Niiranen.
Please tell me more about how you are using Azure and Dynamics CRM together.