Is it possible to set a className on custom react components?

Let's say I have a simple component like this:

class SimpleComponent extends React.Component
{
    render() { return <p>Some text</p> }
}

Is it possible to add a className to SimpleComponent or is this constrained to HTML DOM elements only?

For example:

var mySimpleComponent = <SimpleComponent className="myComp"/>

The reason I would like to do this is so that I can style the elements inside my custom component like this:

.myComp > p {
    background-color: blue;
}

You can, but you should propagate the prop to the inner component. If not, it doesn't know about it.

class SimpleComponent extends React.Component
{
    render() { return <p className={this.props.className}>Some text</p> }
}

To make the CSS query you want to accomplish, then you should create the div inside your component.

class SimpleComponent extends React.Component
{
    render() { return <div className={this.props.className}><p>Some text</p></div> }
}