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 : 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 depreciated but the wp_login action is fine to use.