Having a well thought-out plan for diagnostic data is important for on-premises applications, but it is arguably more important for distributed, highly scalable cloud applications. Michael Collier has provided a clear introduction to Microsoft Azure Diagnostics, including the Diagnostics Agent and how to extract the data.
If your database server is in Azure, then it makes sense to do backups into Azure too. SQL Server 2014 supports backups to the cloud, and particularly well with Managed Backup. Once your backups are safely in an Azure BLOB, then what? Mike Wood takes up the story.