Skyscrapers are huge investments, and the ones who build, design and own them are held responsible for their safety. So extensive amounts of time and money have gone into engineering these buildings to last hundreds of years.
The only unplanned collapse of a skyscaper were the World Trade centers on 9/11. Otherwise, there has been no collapse of a skyscraper. So you should feel just as safe inside them as you are inside your own home.
They are usually built so that the swaying is damped by the building. For very large ones there’s a pendulum or a similar device that absorbs the swimming. It’s the opposite of how you play with a swing (the playground toy) and try to go faster – instead you try to stop yourself from swinging as much as possible (without skidding your feet on the ground, because buildings don’t have that option.)
The shape us also made so that the resonance frequency (the frequency at which the swaying is most impactful) is different from typical swaying in a building. Resonance is also well understood by the swing-example, it’s the rhythm your parents/friends/siblings get into when shoving you to go faster.
Steel frames. They’re strong. Tall Buildings are engineered to withstand a certain limit of windspeeds. Then engineering principles say to apply an amount of over engineering as safety factor, typically 1.5x or 2x
But should we ever get the much speculated tornado that hits the Loop, no amount of over engineering will be enough. Something is gonna come down
Most skyscrapers are built with a series of counterweights in them to help from swaying too much. The buildings are also to designed to sway in the wind. It actually makes them safer.
Imagine a stick that has been dried out. It’s very rigid, but it can be snapped easily. Then take a stick freshly cut from a tree. It can bend quite a bit before it actually breaks. That pliability works the same in the buildings.
Then think about the tall buildings in places like San Francisco and Miami. These buildings can take beatings from massive earthquakes and hurricanes and still stand strong. Windy City wind doesn’t compare to hurricane force winds. So you shouldn’t be concerned at all.
Few different ways. As other people have pointed out, they’ll have weights (Sometimes giant metal balls, sometimes pools of water.) that can weigh hundreds of tons to counteract any sway. Another way though is to shape the building to cope with the wind.
Many skyscrapers will get thinner as you go up since the wind gets faster the higher you go. This is super notice with the [Burj Khalifa](https://upload.wikimedia.org/wikipedia/en/thumb/9/93/Burj_Khalifa.jpg/240px-Burj_Khalifa.jpg) since it really embraces this look. Next, you know how planes and ships will have smoothe edges so they can move through the air/water faster? Well the same applies to stationary buildings. You can go [thin and pointy](https://images.adsttc.com/media/images/5b86/c8b2/f197/cc5a/2500/01da/medium_jpg/Moscow_1.jpg?1535559835) with the pointy end in the same direction as the wind, [twisted and curvy](https://i.pinimg.com/originals/b6/17/8f/b6178fcea46007f052dcdd3809c0599e.jpg) so the wind can flow off the surface instead of hitting it head on, [get really twisted](https://lh4.ggpht.com/-wV8ZNgYRP7k/UXYvEmV7QII/AAAAAAAAnt8/AHPx4cUhYak/evolution-tower-32.jpg?imgmax=800) so the wind hugs the building but pushes itself upward and away, or [literally just punch a hole](https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/%E4%B8%8A%E6%B5%B7%E5%9B%BD%E9%99%85%E9%87%91%E8%9E%8D%E4%B8%AD%E5%BF%83.jpg/240px-%E4%B8%8A%E6%B5%B7%E5%9B%BD%E9%99%85%E9%87%91%E8%9E%8D%E4%B8%AD%E5%BF%83.jpg) in the top so the wind has somewhere to easily go.
Great video by Vox on this: https://youtu.be/ebx5Y5qOmTM
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