Can we use SwiftUi to build iOS Today Extension?

Check this UIHostingController tutorial out, easy, straightforward and works like a charm: https://medium.com/@code_cookies/swiftui-embed-swiftui-view-into-the-storyboard-a6fc96e7a0a1

Create SwiftUI view and integrate it with UIHostingController.

You can do this just like use SwiftUI from UIKit.

Create Today Extension (Widget) with SwiftUI

//
//  WidgetView.swift
//

import SwiftUI

struct WidgetView: View {
    var body: some View {
        HStack {
            Image(systemName: "globe")
            Text("Hello, SwiftUI!")
        }
        .font(.title)
    }
}

//
//  TodayViewController.swift
//

import UIKit
import NotificationCenter
import SwiftUI

class TodayViewController: UIViewController, NCWidgetProviding {

    override func viewDidLoad() {
        super.viewDidLoad()
        // Do any additional setup after loading the view.
        let vc  = UIHostingController(rootView: WidgetView())
        self.addChild(vc)
        self.view.addSubview(vc.view)
        vc.didMove(toParent: self)

        vc.view.translatesAutoresizingMaskIntoConstraints = false
        vc.view.heightAnchor.constraint(equalTo: self.view.heightAnchor).isActive = true
        vc.view.leftAnchor.constraint(equalTo: self.view.leftAnchor).isActive = true
        vc.view.rightAnchor.constraint(equalTo: self.view.rightAnchor).isActive = true
        vc.view.centerYAnchor.constraint(equalTo: self.view.centerYAnchor).isActive = true
        vc.view.backgroundColor = UIColor.clear
    }

    func widgetPerformUpdate(completionHandler: (@escaping (NCUpdateResult) -> Void)) {
        // Perform any setup necessary in order to update the view.

        // If an error is encountered, use NCUpdateResult.Failed
        // If there's no update required, use NCUpdateResult.NoData
        // If there's an update, use NCUpdateResult.NewData

        completionHandler(NCUpdateResult.newData)
    }

}

Using an instance of UIHostingController as your NSExtensionPrincipalClass to instantiate your SwiftUI view should work on iOS 13.

You can now use the new WidgetKit from iOS 14 to build your Widgets using SwiftUI: https://developer.apple.com/documentation/widgetkit/creating-a-widget-extension