After missing their initial target date last week, where they said they expected "to have some services up and running within a week from [April 26]," Sony has stated they should be fully back online by May 31.
If this is the case, the global outage will have lasted a total of six weeks.
On April 20th Sony took the PSN offline after the service was hacked. They recently confirmed to Congress that 77 million PSN accounts have had data stolen due to the intrusion despite rumours that that may not have been the case.