The history of American chimneys is more a history of function than it is a history of style. Prior to widespread use of electricity and gas for cooking and heating, the fireplace was a matter of necessity. The concept of a decorative fireplace simply did not exist. Even in the richest homes, a fireplace might be lavishly constructed. But it had to work as well.
Williamsburg, Virginia can provide some examples of early colonial chimneys. There is a well-preserved Tidewater Colonial house that can serve as an example from 1750. The chimney on this house is built along the outside of the exterior wall to accommodate the deep firebox that it housed. The whole structure is of brick, wide at the base to provide firebox and hearth inside, and then narrowing up to the chimney proper. The chimney proper is separated from the edge of the roof to protect the home from chimney fires.
In 1796, a revolution occurred. Count Rumsford published the his first of two papers describing his new fireplace design. The tall, shallow fireboxes reflected heat more efficiently, and the streamlined throats proved excellent at drawing the smoke up and out. This combination-less depth and a decreased risk of chimney fire-allowed the chimney to be incorporated into the wall of the home rather than attached to the outside.
19th century Victorian chimneys mostly used an adaptation of the Rumsford design. Small, shallow fireplaces burned coal or gas, venting through interior chimneys that went up through the roof. A single chimney could contain two flues, one to vent a coal furnace and the other a shallow gas fireplace. This basic design lasted through World War II.
The 1950s saw the advent of "ranch houses" and central heating. Energy had become cheap. The fireplace was no longer an indispensable part of a home heating strategy. Fireplaces became optional. Less expensive homes didn't include them at all. The homes that did include a fireplace didn't need the fireplace to function as a heater. The fireboxes became broader, spreading out like the rest of the home. And they became deeper, giving a greater feeling of space and keeping the fuel safely back from the carpet. For the first time in over 150 years, chimneys began regularly to be built along the outside walls rather than sent up through the interior.
By the 1970s, many people wanted a fireplace, but they didn't want to pay too much for it. Metal chimneys, sided with treated wood became a popular option. They allowed a decorative fireplace and fire on the inside and didn't look terribly tacky on the outside. People with modest budgets could afford them, and they did. Again, because the firebox was deeper, these chimneys did not run up through the house, but along the outside wall.
Today, you'll see both the cheaper metal chimneys, sometimes encased in artificial brick instead of wood. And you'll see their older, more imposing genuine brick cousins. What you won't see anymore is the good old Rumsford fireplace with interior chimney that held sway for over a hundred years. Even on "period" homes designed to look old-fashioned, the chimney stands out to the trained eye as a modern looking addition running up along the side.