How can I remove wrapper (parent element) without removing the child?

Pure JS (ES2015) solution, in my opinion easier to read than jQuery-solutions.

node.replaceWith(...node.childNodes)

Node has to be an ElementNode

const wrapperNode = document.querySelector('h1')
wrapperNode.replaceWith(...wrapperNode.childNodes)

<h1>
  <a>1</a>
  <b>2</b>
  <em>3</em>
</h1>

Surprised that nobody's posting the simplest answer:

// Find your wrapper HTMLElement
var wrapper = document.querySelector('.wrapper');

// Replace the whole wrapper with its own contents
wrapper.outerHTML = wrapper.innerHTML;

Pure JS solution that doesn't use innerHTML:

function unwrap(wrapper) {
    // place childNodes in document fragment
    var docFrag = document.createDocumentFragment();
    while (wrapper.firstChild) {
        var child = wrapper.removeChild(wrapper.firstChild);
        docFrag.appendChild(child);
    }

    // replace wrapper with document fragment
    wrapper.parentNode.replaceChild(docFrag, wrapper);
}

Try it:

unwrap(document.querySelector('.wrapper'));

Could use this API: http://api.jquery.com/unwrap/

Demo http://jsfiddle.net/7GrbM/

.unwrap

Code will look something on these lines:

Sample Code

$('.button').click(function(){
    $('.wrapper img').unwrap();
});