It has been a long awaited feature, the ability to export recommendations and more importantly alerts from Azure Security Center (ASC).
Well, good news, this feature is now generally available 
To start using it, just logon to your Azure administration portal (https://portal.azure.com/) and reach your Azure Security Center
From there, depending of what you want to download, access either the Recommendations or Security Alerts blade
From there you will find the Download CSV button on top left of the blade
