react-router provides two props for setting a specific style on a Link component whose path matches our current route. activeStyle allows for an inline style while activeClassName allows for an class defined in an external stylesheet.
const Links = () =>
<nav >
<Link activeStyle={{color: 'green'}} to="/">Home</Link>
<Link activeStyle={{color: 'green'}} to="/about">About</Link>
<Link activeClassName="active" to="/contact">Contact</Link>
</nav>;
.active{
color: green;
}