you would need to use the date
query:
$args = array (
'cat' => '1234', // if category being used
'post_type' => 'events', // if custom post type
'paged' => get_query_var('paged'),
'order' => 'DESC',
'paged' => $paged,
'date_query' => array( // this is the thing you need
array(
'before' => array( // this is 'before today'...
'year' => date('Y'),
'month' => date('m'),
'day' => date('d')
),
'inclusive' => true,
),
),
);
$past_events = new WP_Query($args);
category, post type, and date in which you deem to be ‘past’ can be manipulated there.