Yep, I think a lot of a confusing parts of React components is state and ES6 classes. Luckily, you don't actually have to use those, React really shines (IMO) when you write stateless components, using ordinary functions.
const MyList = props => (
<ul>
{props.list.map((item, index) => <li key={index}>{item}</li>)}
</ul>
);
...
<MyList list={[ 'item1', 'item2', 'item3' ]} />