From the Apple documentation:

A UIStoryboardSegue object is responsible for performing the visual transition between two view controllers. In addition, segue objects are used to prepare for the transition from one view controller to another. Segue objects contain information about the view controllers involved in a transition. When a segue is triggered, but before the visual transition occurs, the storyboard runtime calls the current view controller’s prepareForSegue:sender: method so that it can pass any needed data to the view controller that is about to be displayed.

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Attributes

Swift

sourceViewController: UIViewController {get}
destinationViewController: UIViewController {get}
identifier: String? {get}

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References:

• UIViewController Class Reference
• UIStoryBoardSegue Class Reference

PrepareForSegue:

 func prepareForSegue(_ segue:UIStoryboardSegue, sender sender:AnyObject?) 

Notifies the view controller that a segue is about to be performed

Parameters

segue: The segue object.

sender: The object that initialized the segue.

Example in Swift

Perform a task if the identifier of the segue is "SomeSpecificIdentifier"

override func prepareForSegue(segue: UIStoryboardSegue, sender: AnyObject?) {
    if segue.identifier == "SomeSpecificIdentifier" {
        //- Do specific task
    }
}

ShouldPerformSegueWithIdentifier:

 func shouldPerformSegueWithIdentifier(_ identifier:String, sender sender:AnyObject?) -> Bool 

Determines whether the segue with the specified identifier should be performed.

Parameters

Identifier: String that identifies the triggered segue

Sender: The object that initialized the segue.

Example in Swift

Only perform segue if the identifier is "SomeSpecificIdentifier"

override func shouldPerformSegueWithIdentifier(identifier:String, sender:AnyObject?) -> Bool {
    if identifier == "SomeSpecificIdentifier" {
        return true
    }
    return false
}

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Unwind Segues

Unwind Segues give you a way to “unwind” the navigation stack and specify a destination to go back to. The signature of this function is key to Interface Builder recognizing it. It must have a return value of IBAction and take one parameter of UIStoryboardSegue. The name of the function does not matter. In fact, the function does not even have to do anything. It’s just there as a marker of which UIViewController is the destination of the Unwind Segue. [source][1]

Required signature of an unwind segue

Objective C:

-(IBAction)prepareForUnwind:(UIStoryboardSegue *)segue {
}

Swift:

@IBAction func prepareForUnwind(segue: UIStoryboardSegue) {
}

PerformSegueWithIdentifier:

 func performSegueWithIdentifier(_ identifier:String, sender sender:AnyObject?)

Initiates the segue with the specified identifier from the current view controller's storyboard file

Parameters

Identifier: String that identifies the triggered segue

Sender: The object that will initiate the segue.

Example in Swift

Performing a segue with identifier "SomeSpecificIdentifier" from a table view row selection:

func tableView(tableView: UITableView, didSelectRowAtIndexPath indexPath: NSIndexPath) {
    performSegueWithIdentifier("SomeSpecificIdentifier", sender: indexPath.item)
}