When you make use of react-router, you can identify which path you are currently on by simply reading the location.pathname from the props. 
If the component in which you are trying to access location.pathname isn't connected to the Route directly or isn't receiving the Router props, you can wrap it with the withRouter HOC to access router props.
Also, router has a prop called as match which gives the closest match route information to the component that you are using that in 
For example, in a Route configuration
<Route path="/" component={Home} />
Home.jsx
render() {
    console.log(this.props.match.path);
    return (
        <div>
             <Route path="/user" component={User}/>
        </div>
    )
}
So in the above case if you are visiting the url: /user, and if you log this.props.match.url, it will result in / which isn't the desired result that you might be looking for.
A way to get around this is to use matchPath method that is provided by react-router
A typical usage of it would be 
const { match } = this.props;
let { hash } = window.location;
[hash] = hash.slice(1).split('?');
// match.path is the path that is matched till the parent
const customMatch = matchPath(hash, {
    path: `${match.path}user`,
    exact: false,
    strict: false
});
console.log(customMatch)