[Update 04/21/2020] Microsoft has done changes in Productnames

How much storage is available in OneDrive for Business?
Can I get more storage?
What are the limits of storage for OneDrive for Business?
Where is the storage managed?

Actually only a few questions, but the answer is not that easy, and unfortunately also incompletely described by Microsoft. Or not completely. But I suggested that the pages be revised a bit.

How big is the OneDrive storage?

That depends on the respective subscription: We can find this in the admin center. The storage for each licensed user is:

2 GB

Office 365 Enterprise F1
Office 365 Enterprise F3

1 TB

Office 365 Business Essentials Microsoft 365 Business Basic	Office 365 Nonprofit Business Essentials
Office 365 Business	Office 365 Nonprofit Business Premium
Office 365 Business Premium Microsoft 365 Business Standard	Office 365 Nonprofit E1
Office 365 ProPlus Microsoft 365 Apps for Enterprise	OneDrive for Business Plan 1
Office 365 Enterprise E1	SharePoint Online Plan 1
Office 365 Government G1	Microsoft 365 Business Microsoft 365 Business Premium

Beyond 1 TB, to unlimited: Yes, you read it right. „To unlimited„. 1 TB per user for subscriptions with fewer than 5 users. For subscriptions with 5 or more users (can be any combination of qualifying plans), Microsoft will initially provide 1 TB per user, which admins can increase to up to 5 TB per user.

Office 365 Enterprise E3	SharePoint Online Plan 2
Office 365 Enterprise E5	Microsoft 365 Enterprise E3
Office 365 A1	Microsoft 365 Enterprise E5
Office 365 A3	Microsoft 365 A3
Office 365 A5	Microsoft 365 A5
Office 365 US Government G3	Microsoft 365 US Government G3
Office 365 US Government G5	Microsoft 365 US Government G5
Office 365 Non-Profit E3	Microsoft 365 E3 für gemeinnützige Organisationen
Office 365 Non-Profit E5	Microsoft 365 E5 für gemeinnützige Organisationen
OneDrive for Business-Plan 2

When you need cloud storage for individual users beyond the initial 5 TB, admins can open a case with Microsoft technical support to request it. Additional cloud storage will be granted as follows:

When a user has filled their 5 TB of OneDrive storage to at least 90% capacity, Microsoft will increase your default storage space in OneDrive to up to 25 TB per user (admins may set a lower per user limit if they want to).

For any user that reaches at least 90% capacity of their 25 TB of OneDrive storage, additional cloud storage will be provided as 25 TB SharePoint team sites to individual users. This additional storage is provided to the organization by way of credit.

We can find the standard settings for this storage in the Office 365 OneDrive Admin Center, and can increase or decrease it depending on the subscription. This applies to all OneDrive for Business users in your tenant. However, when increasing, the memory is not immediately made available to all users.

A nice calculation example:
Let’s say you are the administrator of 50,000 users of an Office 365 Enterprise E3 plan. The setting is 1 TB (1024 GB). You want to increase the storage space to 2 TB. If this storage space were provisioned immediately, 50,000 1 TB hard drives would have to be available. Or 5000 hard drives with 10 TB volume.

So if you „globally“ increase the memory, you will see different displays, because the memory is only provisioned when a user accesses his OneDrive.

Sometimes you only want to provide certain users with more or less memory. This can then be done using PowerShell. And now it’s getting interesting. Here is another example

We have 500 Office 365 Enterprise E3 standard setting 1 TB
With PowerShell User A we reduce to 250 GB
We are increasing to 2.5 TB with PowerShell User B.
We’re increasing the storage in the Admin console to 2 TB

The question is, what happens to user A and user B memory?

498 Office 365 E3 users now have 2TB *)
User A still has 250 GB
User B still has 2.5 TB

*) Note: As already mentioned above with the provisioning, you will see different results. For Office 365 users who do not work with OneDrive for Business at all, the display will first show 1 TB. Depending on the number of users, it takes a long time. But the memory allocated manually by PowerShell for User A and User B is not changed.

Sources: Microsoft

OneDrive for Business service description
Set the default storage for OneDrive users
Change a specific user’s OneDrive storage space

Thank you to my EX-MVP colleage Sara Barbosa and Wayne Ewington von Microsoft