An idea to fix a broken tile area. Don't tear out the wall of tile, make light of it! Caulk the broken/missing tile to waterproof, then add an air fern (kitchen backsplash) or a fake plant (shower or tub area).
The interior of the Marvilla church in Santarem (Portugal) is covered with azulejos. The most interesting date from 1620 and these are azulejos knows as tapete (carpet style) with multicoloured plant motifs.