Step 1: There is only one thing to import on top:
import {Route} from 'react-router-dom';
Step 2: In your Route, pass the history:
<Route
exact
path='/posts/add'
render={({history}) => (
<PostAdd history={history} />
)}
/>
Step 3: history gets accepted as part of props in the next Component, so you can simply:
this.props.history.push('/');
That was easy and really powerful.