Perched on Castle Hill next to the Fisherman's Bastion, Matthias Church has been a centrepiece of Buda's skyline since the fourteenth century. Its diamond-patterned tiled roof, added during a lavish nineteenth-century restoration by Frigyes Schulek, is instantly recognizable. Inside, the walls and columns are covered in elaborate painted geometric and floral motifs that feel almost Byzantine in their richness. The church served as the coronation site for several Hungarian kings, including Franz Joseph I and Charles IV. There is a small ecclesiastical art museum upstairs worth a quick look. Acoustics are superb, so check for evening organ concerts — hearing one here is a genuine highlight.