How can a web application send push notifications to iOS devices?

To be more specific, in order for a web application to send push notifications to a mobile device, such as the iPhone, the mobile device must have registered to receive push notifications for a particular application. The registration for push notification is done through a native app and can only be performed through a native app. Once the native app is registered for push notification, it can send the authorization token to the server, which can be used in conjunction with the certificate used to provision the native client, to send the push notifications to the mobile device.

As specified in another answer, one option is to 'wrap' your web application in a native application. Meaning that you would create a native application that basically presents a UIWebView (for iPhone dev) to the user showing your web application. While this pretty much functions in the same manner as the native browser, you would be able to add the ability to register for push notifications using the native controls.

It would be beneficial to you to review the Apple's push notification document as it provides some pretty good information on how push messaging functions on the iPhone.

See these links provided by Peter Hosey:

• https://support.apple.com/kb/HT201925
• https://developer.apple.com/library/content/documentation/NetworkingInternet/Conceptual/RemoteNotificationsPG/APNSOverview.html

No, only native iOS applications support push notifications.

UPDATE:
Mac OS X 10.9 & Safari 7 websites can now also send push notifications, but this still does not apply to iOS. Read the Notification Programming Guide for Websites. Also check out WWDC 2013 Session 614.

While not yet supported on iOS (as of iOS 10), websites can send push notifications to Firefox and Chrome (Desktop/Android) with the Push API.

The Push API is used in conjunction with the older Web Notifications to display the message. The advantage is that the Push API allow the notification to be delivered even when the user is not surfing your website, because they are built upon Service Workers (scripts that are registered by the browser and can be executed in background at a later time even after your user has left your website).

The process of sending a notification involves the following:

1. a user visits your website (must be secured over HTTPS): you ask permission to display push notifications and you register a service worker (a script that will be executed when a push notification is received)
2. if the user has granted permission, you can read the device token (endpoint) which should be sent to the server and stored
3. now you can send notifications to the user: your server makes an HTTP POST request to the endpoint (which is an URL that contains the device token). The server which receives the request is owned by the browser manufacturer (e.g. Google, Mozilla): the browser is constantly connected to it and can read the incoming notifications.
4. when the user browser receives a notification executes the service worker, which is responsible for managing the event, retrieving the notification data from the server and displaying the notification to the user

The Push API is currently supported on desktop and Android by Chrome, Firefox and Opera.

You can also send push notifications to Apple / Safari desktop using APNs. The approach is similar, but with many complications (apple developer certificates, push packages, low-level TCP connection to APNs).

If you want to implement the push notifications by yourself start with these tutorials:

• Push API: Push Notifications on the Open Web
• Apple Push Notification system: Configuring Safari Push Notifications

If you are looking for a drop in solution I would suggest Pushpad, which is a service I have built.

Update (September 2017): Apple has started developing the service workers for WebKit (status). Since the service workers are a fundamental technology for web push, this is a big step forward.