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

I am writing a plugin that fetches some extended user info from a remote service and I need it to execute its function each time a user logs in.

Is there a hook that gets fired after login that I can add an action to?

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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 :

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.

and to change the redirect URL after login, there is the filter 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 depreciated but the wp_login action is fine to use.