Long time ago file operations on the blob storage were only possible with PowerShell. Later, the Storage Explorer followed as an application. But now, this tool is available directly as Azure WebApp.
You can access the Azure Storage Explorer directly through Azure Portal:
Via the URL: https://azurestorage.azurewebsites.net you can also access the WebApp directly. There you can authenticate with “Azure Account” and “Key or SAS”.
Are you already using the Web-Version? How are your thoughts?
To download the tool, visit: https://azure.microsoft.com/en-us/features/storage-explorer/
On the following page you will find further improvements to the Azure Experience from September: https://azure.microsoft.com/en-us/blog/azure-user-experience-improvements/