Sony have announced the "full restoration of PlayStation Network services," and yes, that includes the PlayStation Store, promising that all services will be back by the end of the week.
"Sony Corporation and Sony Computer Entertainment (SCE) announced today that Sony Network Entertainment International (SNEI, the company) will fully restore all PlayStation®Network services in the Americas, Europe/PAL territories and Asia, excluding Japan, Hong Kong, and South Korea by the end of this week."
"We have been conducting additional testing and further security verification of our commerce functions in order to bring the PlayStation Network completely back online so that our fans can again enjoy the first class entertainment experience they have come to love," said Kazuo Hirai, Executive Deputy President, Sony Corporation. "We appreciate the patience and support shown during this time."
So there you have it! Don't forget about the Welcome Back programme where every PSN user is eligible for two free PS3 games and two free PSP games if you have the handheld.
Source: PlayStation Blog