How to communicate between iframe and the parent site?

In 2018 and modern browsers you can send a custom event from iframe to parent window.

iframe:

var data = { foo: 'bar' }
var event = new CustomEvent('myCustomEvent', { detail: data })
window.parent.document.dispatchEvent(event)

parent:

window.document.addEventListener('myCustomEvent', handleEvent, false)
function handleEvent(e) {
  console.log(e.detail) // outputs: {foo: 'bar'}
}

PS: Of course, you can send events in opposite direction same way.

document.querySelector('#iframe_id').contentDocument.dispatchEvent(event)

With different domains, it is not possible to call methods or access the iframe's content document directly.

You have to use cross-document messaging.

parent -> iframe

For example in the top window:

myIframe.contentWindow.postMessage('hello', '*');

and in the iframe:

window.onmessage = function(e) {
    if (e.data == 'hello') {
        alert('It works!');
    }
};

For example in the top window:

window.onmessage = function(e) {
    if (e.data == 'hello') {
        alert('It works!');
    }
};

and in the iframe:

window.top.postMessage('hello', '*')