wordpress get current taxonomy
snippet in php

get current term id

user9537

<?php $current_term = get_queried_object()->term_id; ?>

wordpress get current taxonomy

user5029

$term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
echo $term->name; // will show the name
echo $term->slug; // will show the slug