WP: Get current taxonomy

// get current taxonomy-slug in template taxonomy-{taxonomy}.php
$term = get_term_by('slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) );
echo $term->slug;

// get full info of taxonomy
$the_tax = get_taxonomy( get_query_var( 'taxonomy' ) );
echo $the_tax->labels->name;

// get taxonomy-type current
echo get_query_var('taxonomy');