React.js, syntax for handling promises?

what is the best way to handle promises in React.js? The code below works - is there a more reacty way?

handleFormSubmit(input){

    this.setState({
        originId: input.originId,
        destinationId: input.destinationId,
        radius: input.radius,
        search: input.search
    });

    var routeSearch = new FindRoutes({
        originPlaceId: input.originId,
        destinationPlaceId: input.destinationId,
        directionsDisplay: directionsDisplay,
        directionsService: directionsService,
        travel_mode: google.maps.TravelMode.DRIVING,
        search: input.search
    });

    routeSearch.execute()
    .then(function(){
        alert("promise fullfilled!");
    });

}