Display Sub-categories or Child Pages of Parent Cat/Page?

for sub-pages of current page
check wp_list_pages()

<?php 
  $page_id = get_the_ID();
  wp_list_pages( array( 'child_of'=>$page_id ) );
?> 

and for sub-categories of the parent category check wp_list_categories()

<?php 
$cat_id = get_query_var('cat');
if( !empty($cat_id) ) {
  wp_list_categories( array( 'child_of'=> $cat_id ) );
}
?>