The National Tile Museum is five centuries of azulejo, and it lives in a convent. Its church is one of the richest interiors in Lisbon, and the nuns' upper choir looks down into it from the far end. The collection runs from fifteenth-century Moorish geometry to work made in the last few years, and it is arranged so that you walk through the change one room at a time. Upstairs, one wall carries the Great Panorama.
The rest of the museum is the story of how a single material took over a country. Follow the tile out of the galleries and it turns up on church walls, palace stairs, house fronts, shopfronts and, in the last few decades, metro platforms. The collection moved into this convent in 1965. The real effect of the visit shows up outside on the walk back, when the tiled house fronts you passed on the way in stop being background.