Years ago I saw a house that despite there being no gutters, there was still downspouts running down from the roof. I assumed the gutter must have fallen in a snow storm or something.
Later I discovered that this house did actually have a working gutter. It was just that the gutter was not exposed but hidden. This is why this set-up is called a "Concealed roof drainage system" but better known as a "Built in gutter". This type of gutter was created to be hidden so that it doesn't take away the character or historic design of the house.
More recently I had the dubious pleasure of replacing a built in gutter on a house in Newton. Doing this was not an easy job. I had to cut out and remove the copper lining. The new gutter lining had to be shaped and soldered together by a copper expert. When I installed the new copper I had to seal it in to the existing EPDM rubber roof.
Built in gutters are almost always made of copper and are shaped into a shallow but wide trough. This shape makes them less apt to clog. The shallowness of this gutter allows the wind to circle through, resulting in leaves being blown out and removed.
Today, you don't see many of the built in gutter systems. The weak points are the joints on the copper seams, and once they begin to leak they can't be re-soldered. Because replacing the copper lining is so expensive, the majority of homeowners will not replace them. When it is time to replace the roof, often the owner will have the contractor roof over the hidden gutter, never to be seen again.