Wordpress - Is there a hook that runs after a user logs in?

The action hook wp_login runs when the user logs in - it can run a simple function.

function do_anything() {
    //do stuff
}
add_action('wp_login', 'do_anything');

documentation : https://codex.wordpress.org/Plugin_API/Action_Reference/wp_login

The real breadwinner here is wp_authenticate which has a bit of documentation. It passes an array with the given username and password, which gives you the opportunity to pass info to the remote service, if necessary. https://codex.wordpress.org/Plugin_API/Action_Reference/wp_authenticate

and to change the redirect URL after login, there is the filter login_redirect: https://codex.wordpress.org/Plugin_API/Filter_Reference/login_redirect

I would caution against using wp_login. It is deprecated and in later versions of WordPress it may not work at all. Instead try the wp_signon function.

Edit: The wp_login function is deprecated but the wp_login action is still fine to use.