gistfile1.js

/** @jsx React.DOM */

var Bubbler = React.createClass({
  render: function() {
    return <input type="button" onClick={this.props.onFoo} value="Click me"/>;
  }
});

var Handler = React.createClass({
    onFoo: function() {
      alert("handled!");
    },
    render: function() {
        return <Bubbler onFoo={this.onFoo}/>;
    }
});
 
React.renderComponent(<Handler/>, document.body);

gistfile2.js

/** @jsx React.DOM */

var Bubbler = React.createClass({
  render: function() {
    return <input type="button" onClick={this.props.onFoo} value="Click me"/>;
  }
});

var Handler = React.createClass({
    effects: {
        foo: function() {
            alert("handled!");
        }
    },
    render: function() {
        return <Bubbler onFoo={this.effects.foo}/>;
    }
});
 
React.renderComponent(<Handler/>, document.body);

gistfile3.js

/** @jsx React.DOM */

var Bubbler = React.createClass({
  render: function() {
    return <input type="button" onClick={this.props.onFoo} value="Click me"/>;
  }
});

var Handler = React.createClass({
    handlers: function() {
        return [
            [this.props.eff, function() {
                alert("handled!");
            }]
        ];
    },
    render: function() {
        return this.props.children;
    }
});

var Wrapper = React.createClass({
  effects: {
    foo: newEffect()
  },
  render: function() {
    return <Handler eff={this.effects.foo}><Bubbler onFoo={this.effects.foo}/></Handler>
  }
});
 
React.renderComponent(<Wrapper/>, document.body);

I ended up implementing the range thing I was talking about https://davidbruant.github.io/inline-range-demo/ Click on the number and drag left and right to increase/decrease the value.
It can be implemented in React, but in a way that is more elegant in my opinion, because of the lack of a proper event system.

http://jsbin.com/vapay/4/edit

It's really matter of calling the handleMouseMove method and testing for this.state.dragging; it's probably less performent, but not that much I think (though I'm not sure). This could probably be microbenchmarked, oh well.