At least 5 lawsuits have been filed against Target in the wake of a security breach.
They allege the retailer should have done more to prevent thieves from stealing customers' data.
40 million shoppers were affected.
At least one person is seeking millions of dollars in damages.
The retailer, meanwhile, has been trying to control the damage to its sales.
This weekend it offered 10 percent discounts to all customers and it's offered free credit monitoring services to affected customers, but the problems may be just beginning.
A security blog claims many of the stolen cards have been sold on the black market in recent weeks.
According to industry experts, customers whose information was hacked won't be financially liable.
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