If you need to add the state color as className to "cheese" then you can do it like
<button className={"cheese " + this.state.color}>
Working code
var Hello = React.createClass({ getInitialState: function(){ return { color: 'blue' }; }, handleClick: function(){ if (this.state.color === 'blue'){ this.setState({color: 'green'}); } else { this.setState({color: 'blue'}); } }, render: function() { return <button className={"cheese " + this.state.color} onClick={this.handleClick}>My background is: {this.state.color}, Click me to change</button>; } }); React.render(<Hello name="World" />, document.getElementById('container'));
JSFIDDLE