At react conf 2015, Ryan Florence demonstrated using portals. Here’s how you can create a simple Portal component…

var Portal = React.createClass({
  render: () => null,
  portalElement: null,
  componentDidMount() {
    var p = this.props.portalId && document.getElementById(this.props.portalId);
    if (!p) {
      var p = document.createElement('div');
      p.id = this.props.portalId;
      document.body.appendChild(p);
    }
    this.portalElement = p;
    this.componentDidUpdate();
  },
  componentWillUnmount() {
    document.body.removeChild(this.portalElement);
  },
  componentDidUpdate() {
    React.render(<div {...this.props}>{this.props.children}</div>, this.portalElement);
  }
});

and then everything you can normally do in React you can do inside of the portal…

    <Portal className="DialogGroup">
       <ReactCSSTransitionGroup transitionName="Dialog-anim">
         { activeDialog === 1 && 
            <div key="0" className="Dialog">
              This is an animated dialog
            </div> }
       </ReactCSSTransitionGroup>
    </Portal> 

jsbin demo

You can also have a look at Ryan’s react-modal, although I haven’t actually used it so I don’t know how well it works with animation.