I've been doing a lot of work, recently, around Azure – and one interesting aspect is Azure Storage. Azure Storage enables you to store and retrieve large amounts of unstructured data, such as documents and media files with Azure Blobs; structured nosql based data with Azure Tables; reliable messages with Azure Queues and use SMB-based Azure Files that can help to migrate on-premises applications to the cloud. The first three of these feature have been offered by Azure for several years, while Azure Files is newer. Azure files is still in preview – and you can learn a bit more about the File Service from the Azure Strorage team's team blog.
As an aside, the Azure module you can download enables you to manage Azure Storage features from PowerShell. The cmdlet set is rich (and richer with Azure Files) with 48 storage related cmdlets in the latest version of the Azure Cmdlets (0.8.12). These cmdlets are fairly easy to use, but I've found the error handling is a bit harder than with equivalent on-premise cmdlets. Many errors, for instance, return little useful information to help you troubleshoot. There is room for improvement – and knowing the Azure team, will come as fast as they can get to it!
In order both to scale and to provide great recovery from failure, the architecture of Azure storage is a bit more complex than the NTFS file system we are used to. Although it's now a couple of years old, the Azure team also published a detailed description of the Azure Storage Architecture. It's true level 400 stuff – and you can find it here. The paper does not cover the Azure File Service – hopefully Microsoft will provide an update to this great white paper at some point in the future.
If you are planning on architecting solutions utilising Azure Storage, this paper is one you should read and absorb. And, in due course, apply when you implement your solution(s)!