How can I access the current route from anywhere in my app?

this is very simple. You can use withRouter HOC

You can access the properties of the history object and the closest Route match via the withRouter higher-order component . Whenever rendered, withRouter will pass the updated match, position and history props to the wrapped component.

like to use it like this:

import {withRouter} from "react-router-dom"
@withRouter
class NonRouteComponent extends Component {
  render() {
    // you have access to this.props.match
    // you have access to this.props.history
    // you have access to this.props.location
    const { match, location, history } = this.props

    return <h1>Hi {location.pathname}</h1>;
  }
}

If you don't use the decorator (aka @withRouter), you can export the component like this:

class NonRouteComponent extends Component { ... }
export default withRouter(NonRouteComponent);