Audit logs are moved from SharePoint site collection to Office 365 Security and Compliance Center.
I.e. to view Audit Logs in on-prem you have to go to the site collection and get audit logs for this site collection.
In Office 365 it is different:
1) no audit logs within site collection
2) Search for tenant-level Audit logs now available from Office 365 Security and Compliance Center
So in Office 365 the one who have tenant SharePoint Administrator role cannot get audit logs.
Question: What kind of permissions (roles) required to be able to see audit logs?
Answer: "View-Only Audit Logs" role assigned in Exchange Online admin Center.
No any global admin role is required. I.e. any non-admin user can see audit logs (and more).
Trick: you must go directly to https://protection.office.com/unifiedauditlog.
If you try to login to http://admin.microsoft.com/ (having in mind to go to SCC), you'll get "You don’t have permission to access this page or perform this action" message.
But if you go directly to https://protection.office.com/unifiedauditlog, you'll see audit logs.