How to Add Live Camera Preview to UIView

iOS 13/14 and Swift 5.3:

private var imageVC: UIImagePickerController?

and then call showCameraVC() when you want to show the camera view

func showCameraVC() {    
    self.imageVC = UIImagePickerController()

    if UIImagePickerController.isCameraDeviceAvailable(.front) {
        self.imageVC?.sourceType = .camera
        self.imageVC?.cameraDevice = .front
        self.imageVC?.showsCameraControls = false
                
        let screenSize = UIScreen.main.bounds.size
        let cameraAspectRatio = CGFloat(4.0 / 3.0)
        let cameraImageHeight = screenSize.width * cameraAspectRatio
        let scale = screenSize.height / cameraImageHeight
        self.imageVC?.cameraViewTransform = CGAffineTransform(translationX: 0, y: (screenSize.height - cameraImageHeight)/2)
        self.imageVC?.cameraViewTransform = self.imageVC!.cameraViewTransform.scaledBy(x: scale, y: scale)
    
        self.imageVC?.view.frame = CGRect(x: 0, y: 0, width: screenSize.width, height: screenSize.height)
        self.view.addSubview(self.imageVC!.view)
        self.view.sendSubviewToBack(self.imageVC!.view)
    }
}

Camera view will be also fullscreen (other answers wouldn't fix a letterboxed view)

UPDATED TO SWIFT 5

You can try something like this:

import UIKit
import AVFoundation

class ViewController: UIViewController{
    var previewView : UIView!
    var boxView:UIView!
    let myButton: UIButton = UIButton()

    //Camera Capture requiered properties
    var videoDataOutput: AVCaptureVideoDataOutput!
    var videoDataOutputQueue: DispatchQueue!
    var previewLayer:AVCaptureVideoPreviewLayer!
    var captureDevice : AVCaptureDevice!
    let session = AVCaptureSession()

    override func viewDidLoad() {
        super.viewDidLoad()
        previewView = UIView(frame: CGRect(x: 0,
                                           y: 0,
                                           width: UIScreen.main.bounds.size.width,
                                           height: UIScreen.main.bounds.size.height))
        previewView.contentMode = UIView.ContentMode.scaleAspectFit
        view.addSubview(previewView)

        //Add a view on top of the cameras' view
        boxView = UIView(frame: self.view.frame)

        myButton.frame = CGRect(x: 0, y: 0, width: 200, height: 40)
        myButton.backgroundColor = UIColor.red
        myButton.layer.masksToBounds = true
        myButton.setTitle("press me", for: .normal)
        myButton.setTitleColor(UIColor.white, for: .normal)
        myButton.layer.cornerRadius = 20.0
        myButton.layer.position = CGPoint(x: self.view.frame.width/2, y:200)
        myButton.addTarget(self, action: #selector(self.onClickMyButton(sender:)), for: .touchUpInside)

        view.addSubview(boxView)
        view.addSubview(myButton)

        self.setupAVCapture()
    }

    override var shouldAutorotate: Bool {
        if (UIDevice.current.orientation == UIDeviceOrientation.landscapeLeft ||
        UIDevice.current.orientation == UIDeviceOrientation.landscapeRight ||
        UIDevice.current.orientation == UIDeviceOrientation.unknown) {
            return false
        }
        else {
            return true
        }
    }

    @objc func onClickMyButton(sender: UIButton){
        print("button pressed")
    }
}


// AVCaptureVideoDataOutputSampleBufferDelegate protocol and related methods
extension ViewController:  AVCaptureVideoDataOutputSampleBufferDelegate{
     func setupAVCapture(){
        session.sessionPreset = AVCaptureSession.Preset.vga640x480
        guard let device = AVCaptureDevice
        .default(AVCaptureDevice.DeviceType.builtInWideAngleCamera, 
                 for: .video,
                 position: AVCaptureDevice.Position.back) else {
                            return
        }
        captureDevice = device
        beginSession()
    }

    func beginSession(){
        var deviceInput: AVCaptureDeviceInput!

        do {
            deviceInput = try AVCaptureDeviceInput(device: captureDevice)
            guard deviceInput != nil else {
                print("error: cant get deviceInput")
                return
            }

            if self.session.canAddInput(deviceInput){
                self.session.addInput(deviceInput)
            }

            videoDataOutput = AVCaptureVideoDataOutput()
            videoDataOutput.alwaysDiscardsLateVideoFrames=true
            videoDataOutputQueue = DispatchQueue(label: "VideoDataOutputQueue")
            videoDataOutput.setSampleBufferDelegate(self, queue:self.videoDataOutputQueue)

            if session.canAddOutput(self.videoDataOutput){
                session.addOutput(self.videoDataOutput)
            }

            videoDataOutput.connection(with: .video)?.isEnabled = true

            previewLayer = AVCaptureVideoPreviewLayer(session: self.session)
            previewLayer.videoGravity = AVLayerVideoGravity.resizeAspect

            let rootLayer :CALayer = self.previewView.layer
            rootLayer.masksToBounds=true
            previewLayer.frame = rootLayer.bounds
            rootLayer.addSublayer(self.previewLayer)
            session.startRunning()
        } catch let error as NSError {
            deviceInput = nil
            print("error: \(error.localizedDescription)")
        }
    }

    func captureOutput(_ output: AVCaptureOutput, didOutput sampleBuffer: CMSampleBuffer, from connection: AVCaptureConnection) {
        // do stuff here
    }

    // clean up AVCapture
    func stopCamera(){
        session.stopRunning()
    }

}

Here i use a UIView called previewView to start the camera and then i add a new UIView called boxView wich is above previewView. I add a UIButton to boxView

IMPORTANT

Remember that in iOS 10 and later you need to first ask the user for permission in order to have access to the camera. You do this by adding a usage key to your app’s Info.plist together with a purpose string because if you fail to declare the usage, your app will crash when it first makes the access.

Here's a screenshot to show the Camera access request

Swift 4

Condensed version of mauricioconde's solution

You can use this as a drop in component:

//
//  CameraView.swift

import Foundation
import AVFoundation
import UIKit

final class CameraView: UIView {

    private lazy var videoDataOutput: AVCaptureVideoDataOutput = {
        let v = AVCaptureVideoDataOutput()
        v.alwaysDiscardsLateVideoFrames = true
        v.setSampleBufferDelegate(self, queue: videoDataOutputQueue)
        v.connection(with: .video)?.isEnabled = true
        return v
    }()

    private let videoDataOutputQueue: DispatchQueue = DispatchQueue(label: "JKVideoDataOutputQueue")
    private lazy var previewLayer: AVCaptureVideoPreviewLayer = {
        let l = AVCaptureVideoPreviewLayer(session: session)
        l.videoGravity = .resizeAspect
        return l
    }()

    private let captureDevice: AVCaptureDevice? = AVCaptureDevice.default(.builtInWideAngleCamera, for: .video, position: .back)
    private lazy var session: AVCaptureSession = {
        let s = AVCaptureSession()
        s.sessionPreset = .vga640x480
        return s
    }()

    override init(frame: CGRect) {
        super.init(frame: frame)

        commonInit()
    }

    required init?(coder aDecoder: NSCoder) {
        super.init(coder: aDecoder)

        commonInit()
    }

    private func commonInit() {
        contentMode = .scaleAspectFit
        beginSession()
    }

    private func beginSession() {
        do {
            guard let captureDevice = captureDevice else {
                fatalError("Camera doesn't work on the simulator! You have to test this on an actual device!")
            }
            let deviceInput = try AVCaptureDeviceInput(device: captureDevice)
            if session.canAddInput(deviceInput) {
                session.addInput(deviceInput)
            }

            if session.canAddOutput(videoDataOutput) {
                session.addOutput(videoDataOutput)
            }
            layer.masksToBounds = true
            layer.addSublayer(previewLayer)
            previewLayer.frame = bounds
            session.startRunning()
        } catch let error {
            debugPrint("\(self.self): \(#function) line: \(#line).  \(error.localizedDescription)")
        }
    }

    override func layoutSubviews() {
        super.layoutSubviews()
        previewLayer.frame = bounds
    }
}

extension CameraView: AVCaptureVideoDataOutputSampleBufferDelegate {}