Constrained View Controller extension which displays a "No Internet Connection" message when reachability is lost. To use it simply extend your existing ViewController and make it implement ReachabilityAware and call the startMonitoryReachability() method.

ReachabilityAware.swift

// Constrained View Controller extension which display a "No Internet Connection" message when reachability is lost.
// This implementation depends on ReachabilitySwift (https://github.com/ashleymills/Reachability.swift).
// It can easily enough be adapted to other frameworks. 
// Assumes you have a localized string with the key "warning.no_internet_connection" in one of your .strings files.
// Call startMonitoringReachability() in viewWillAppear and stopMonitoringReachability() in viewDidDisappear

import ReachabilitySwift

protocol ReachabilityAware {
    func startMonitoringReachability()
    func stopMonitoringReachability()
}

extension ReachabilityAware where Self: UIViewController {
    
    private var reachability: Reachability? {
        get {
            if let reach = objc_getAssociatedObject(self, &AssociatedKeys.ReachabilityKey) as? Reachability {
                return reach
            }
            
            do {
                let reach = try Reachability.reachabilityForInternetConnection()
                objc_setAssociatedObject(self, &AssociatedKeys.ReachabilityKey, reach, .OBJC_ASSOCIATION_RETAIN_NONATOMIC)
                return reach
            }
            catch let error {
                print("Error creating reachability \(error)")
                return nil
            }
        }
    }
    
    func startMonitoringReachability() {
        reachability?.whenUnreachable = { reachability in
            self.becameUnreachable()
        }
        
        reachability?.whenReachable = { reachability in
            self.becameReachable()
        }
        
        do {
            try reachability?.startNotifier()
        } catch let error {
            print("Unable to start reachability notifier with error \(error)")
        }
        
        let isInitiallyReachable = reachability?.isReachable() ?? false
        isInitiallyReachable ? becameReachable() : becameUnreachable()
    }
    
    func stopMonitoringReachability() {
        reachability?.stopNotifier()
    }
    
    private func becameUnreachable() {
        if self.view.viewWithTag(Tags.NoInternetViewTag) != nil {
            return
        }
        
        let label = UILabel()
        label.text = NSLocalizedString("warning.no_internet_connection", comment: "No Internet Connection")
        label.textColor = UIColor.whiteColor()
        label.backgroundColor = UIColor.blackColor()
        label.textAlignment = .Center
        label.font = UIFont.systemFontOfSize(12.0)
        label.tag = Tags.NoInternetViewTag
        
        self.view.addSubview(label)
        label.translatesAutoresizingMaskIntoConstraints = false
        
        self.view.addConstraints([
            NSLayoutConstraint(item: label, attribute: .Leading, relatedBy: .Equal, toItem: view, attribute: .Leading, multiplier: 1, constant: 0),
            NSLayoutConstraint(item: label, attribute: .Trailing, relatedBy: .Equal, toItem: view, attribute: .Trailing, multiplier: 1, constant: 0),
            NSLayoutConstraint(item: label, attribute: .Bottom, relatedBy: .Equal, toItem: view, attribute: .Bottom, multiplier: 1, constant: 0)
        ])
        
        label.addConstraint(NSLayoutConstraint(item: label, attribute: .Height, relatedBy: .Equal, toItem: nil, attribute: .NotAnAttribute, multiplier: 1, constant: 20))
    }
    
    private func becameReachable() {
        if let label = self.view.viewWithTag(Tags.NoInternetViewTag) {
            UIView.animateWithDuration(0.25,
                animations: { _ in
                    label.transform = CGAffineTransformMakeTranslation(0, label.frame.height)
                },
                completion: { complete in
                    if complete {
                        label.removeFromSuperview()
                    }
            })
        }
    }
}

private struct Tags {
    static var NoInternetViewTag = 123
}

private struct AssociatedKeys {
    static var ReachabilityKey = "reachability_key"
}