There are no Exceptions in Swift, similar to Objective-C's approach.
In development, you can use assert to catch any errors which might appear, and need to be fixed before going to production.
The classic NSError approach isn't altered, you send an NSErrorPointer, which gets populated.
Brief example:
var error: NSError?
var contents = NSFileManager.defaultManager().contentsOfDirectoryAtPath("/Users/leandros", error: &error)
if let error = error {
println("An error occurred \(error)")
} else {
println("Contents: \(contents)")
}