handling login/logout redirects

I have a couple issues with the way WordPress handles redirects on login and logout.

Standard behaviour is:

login: /wp-login.php (with no redirect_to url) -> /wp-admin.php 
logout: /wp-admin.php -> /wp-login.php

What want is:

login: /wp-login.php (with no redirect_to url) -> homepage
logout: /wp-admin.php -> homepage

Would prefer a coded solution please. It helps me to learn and understand how WordPress works.

Thank you

This really does belong in a plugin, but you can just as easily drop it in your theme’s functions.php

function default_login_redirect( $redirect, $request_redirect )
{
    if ( $request_redirect === '' )
        $redirect = home_url();
    return $redirect; 
}
add_filter( 'login_redirect', 'default_login_redirect', 10, 2 );