Range Hoods
The hood sits right above the backsplash, so it is chosen together with the tile. Size it at least as wide as the cooktop, and choose the airflow for the kind of cooking you do.
Wall mount hoods leave the backsplash on show up to the ceiling. Insert hoods hide inside custom cabinetry. Island hoods hang from the ceiling over a cooktop in the island. See kitchen backsplash tile for the wall behind it.