The structure that inherited the title of world's tallest from the Eiffel Tower requires a bit of a backstory.
Just as Blue Whales did not emerge from dinosaurs but rather from fuzzy little mammals, the skyscrapers of today did not emerge from the lineage of pyramids or cathedrals.
Rather the ancestor of the skyscraper was a small building in Chicago that doesn't exist anymore. When it was built in 1885 it wasn't all that out of place in Chicago. There were already taller buildings in the city
Home Insurance Building
Year Completed: 1885
Height: 138 feet initially, increased to 180 feet in 1890 when two floors were added.
Claim to Fame: The Home Insurance Building was different.
It was the fuzzy little mammal whose descendants would dominate the skyline of cities from Boston to Bangkok. The masonry dinosaurs were on the way out just as stoneworking had reached its ultimate glory in Hamburg and Rouen.
The Home Insurance Building was just ten storeys tall, but it was the first office building whose weight was supported by a steel frame rather than the walls of the structure. Because the walls did not have to support the weight, they were actually made of a thin layer of brick called a "curtain wall" that just cladded the frame and held up nothing but itself. The architect was engineer William LeBaron Jenney.
Curtain-wall construction meant that the Home Insurance Building weighed only one-third as much as a stone building of the same size would have. Chicago officials were so concerned that this new way of building might be unsafe (its walls are too thin! It will fall down!) that they halted construction for almost six months in 1884 while they investigated the safety of the building.
^From small beginnings: The 180-foot tall Home Insurance Building was never even the tallest building of Chicago, but it was the ancestor of all skyscrapers to come.
At the time the Home Insurance Building was built, few apartment and office buildings were more than five storeys tall, although there were some buildings as tall as seven or ten storeys in Amsterdam and other crowded cities in Europe.
The cheap apartments were on the higher floors, because walking up so many stairs was a chore.
But the main limiting factor on height was the weight of masonry. The taller a building was, the thicker the masonry at the base had to be. The great Cathedrals solved this problem by enclosing huge open spaces with arches and then filling the gaps between the arches with stained glass windows. Even then, buttresses had to extend out to the sides of cathedrals to distribute the weight.
This concept is fairly useless for a multi-storey building, because cathedral design cannot support floors running through the big central space that can hold any weight. The side walls of the cathedral can only hold up themselves. This is why cathedrals can be tall, but they are also mostly hollow.
So other than clock towers (mostly based on cathedral design anyway) the tallest structures in every city were always church steeples.
As fate would have it, Chicago is home to the tallest building ever built that does not have a metal skeleton:
The 17-storey Monadnock Building stands 197 feet tall, and was built in two stages between 1889 and 1893. To support the weight of the building, the walls at the base are more than six feet thick!
This is as tall as anyone ever bothered to build a load-bearing office building. (But Philly City Hall is the all-time record holder for a large masonry building)
In contrast, the 180-foot Home Insurance building had walls that were less than two feet thick from the bottom to the top. And they didn't have to be even that thick anyway. You could cover the steel skeleton with paper mache if you felt like it, since they didn't have anything to do with holding up the building.
By combining curtain walls and a steel frame with new technology such as elevators and pumps to provide water to the higher floors, the sky became the limit. Within a few years of the Home Insurance Building opening, other skyscrapers appeared in Chicago and, of course, New York City where land was so very scarce.
The first New York skyscraper in the "Chicago style" was the 16-storey (187-foot) New York Times Building of 1889.
Not to be outdone, the New York World newspaper commissioned a giant structure to dwarf the head office of its rival:
New York World Building
Location: New York City
Constructed: 1890
Height: 309 feet to the top of the dome, plus a 40-foot spire for a total of 349 feet.
Claim to Fame: With twenty storeys, the World Building had more floors than any other building... in the World. Including the spire, it was almost twice the height of the Home Insurance Building in Chicago, and from here on the tallest buildings on Earth would all be in New York City.
It should be noted however, that although it was the tallest office building, it was not the tallest structure in New York City when it was built. The 338-foot spires of St. Patrick Cathedral and the caissons of the Brooklyn Bridge were actually taller.
Still,
the skyscraper had arrived.
Status: The World Building was demolished in 1955 to allow an expansion of the car ramp leading to the Brooklyn Bridge. The Home Insurance Building also no longer exists, having been demolished in 1931 to make way for a larger office building.