React: Access element's text

You use the children property, which contains the children of your element (which might be text or an array of children [I think it's always an array when it's not text], see the link for the gory details). E.g.:

const Foo = props => {
  console.log(props.children);
  return (
    <div>{props.children}</div>
  );
};
ReactDOM.render(
  <Foo>Hi There</Foo>,
  document.getElementById("react")
);
<div id="react"></div>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>

That uses a stateless functional component (SFC), but it's the same for Component subclasses:

class Foo extends React.Component {
  render() {
    console.log(this.props.children);
    return (
      <div>{this.props.children}</div>
    );
  }
};
ReactDOM.render(
  <Foo>Hi There</Foo>,
  document.getElementById("react")
);
<div id="react"></div>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>

Here's an example of the fact that children isn't just for text:

class Foo extends React.Component {
  render() {
    console.log(this.props.children);
    return (
      <div>{this.props.children}</div>
    );
  }
};
ReactDOM.render(
  <Foo>
    <div>Hi there</div>
    <Foo><span>nested Foo > Foo > span</span></Foo>
  </Foo>,
  document.getElementById("react")
);
<div id="react"></div>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>