UPDATED 12:30PM: The PlayStation Europe Twitter feed currently says that PSN has been restored in New Zealand, but PC World readers have been reporting that they still cannot access their accounts (see comments below).
Service is likely to be intermittent while the company copes with heavy traffic.
Original story: After nearly four weeks, the PlayStation Network is finally coming back online in New Zealand, Australia, South America, Europe and the US.
PSN customers are now able to to install a firmware update and change their account password.
"Please note that these services will take a bit of time to be turned on and rolled out to the whole region. The process has begun and some countries are being turned on now, so please be patient as we reach you," Sony said in the PlayStation Europe blog.
Restoration will be phased, beginning with online gaming services.
The network was taken down by Sony after hackers compromised the network's security and accessed the personal information - and potentially credit card details - of millions of users.
Shortly afterward, Sony Online Entertainment's Station.com was also taken down for similar reasons. Sony said at the time that more than 12,000 credit card numbers had been stolen from Station.com users, but those details were from 2007.