On My Pages you can see the authorisation you have by clicking on "Hefur umboð fyrir". This also lists expired authorisations.
You can also see who you've authorised to handle matters by clicking "Veitt umboð".
Your authorisation level depends on which role was selected during authorisation.
These roles are:
General authorisation (Allsherjarumboð): Authorised to see everything on Island.is My Pages, including the inbox.
Inbox (Pósthólf): Authorised to read messages in the Island.is inbox.
Payroll manager (Launafulltrúi): Authorised to manage employer claims under "Finance" showing employee duties other than taxes withheld from paycheck.
Accountant (Bókari): Authorised to view payment status of duties paid to the government, movements, claims, and receipts under "Finance". Municipalities' employees are authorised to view municipal income taxes.
CFO (Fjármálastjóri): Authorised to view everything under "Finance", i.e. duties and taxes, movements, claims, receipts and employer claims. A CFO of a municipality can also see municipal income taxes.
Consultation portal (Samráðsgátt): Authorised to submit statements for a legal entity.
Referee system (Umsagnarkerfi): Authorised as a referee for the Island.is licensing portal.
Application system (Umsóknarkerfi): Authorised to submit applications as an applicant for a legal entity. This is the most common authorisation, it is needed for all applications that require authentication via electronic ID.
Administration system (Umsýslukerfi): Access to license applications.
Security breach (Öryggisbrestur): Authorised to submit notifications of a security breach.
Service provider
Digital Iceland