list taxonomy terms in current post / current category

You can try this:

/**
 * List the taxonomies and terms for a given post
 * 
 * @param int $post_id
 * @return string
 */
function get_the_current_tax_terms_wpse( $post_id )
{
    // get taxonomies for the current post type
    $taxonomies = get_object_taxonomies( get_post_type( $post_id ) );

    $html = "";
    foreach ( (array) $taxonomies as $taxonomy) 
    {        
        // get the terms related to the post
        $terms = get_the_terms( $post->ID, $taxonomy );
        if ( !empty( $terms ) )
        {
            $li = '';        
            foreach ( $terms as $term )
                $li .= sprintf( '<li><a href="%s">%s</a></li>', 
                                 get_term_link( $term->slug, $taxonomy ),
                                 $term->name );

             if( ! empty ( $li ) )
                 $html .= sprintf( '<li><ul><li>%s:</li>%s</ul></li>', 
                                    $taxonomy, 
                                    $li );
        }
    }
    return sprintf( '<ul>%s</ul>', $html );
}

where you can call it with:

echo get_the_current_tax_terms_wpse( get_the_ID() );

from your template.