Updating post content on the front end

I have used the code below to add frontend editing to my posts/pages. How would I go about saving the post content when an update/save button is pressed?

$post_id = get_the_ID();

$settings = array(
'wpautop' => true,
'media_buttons' => true,
'wpautop' => true,
'tinymce' => true,
'quicktags' => true,
'textarea_rows' => 18
);

$post = get_post($post_id, 'OBJECT');
wp_editor($post->post_content, 'epicpagecontent', $settings );

<input type="submit" name="submit" id="submit" value="Update">