It's not necessarily the answer to your query but when people talk about the 20th Century then I can't help but think of the song Twentieth Century by the Pet Shop Boys because I've listened to it enough to make that my first association with the term.
I do like the song and it's softer reflective sound which works well with the lyrics as Neil Tennant sings about his lesson from the Twentieth Century. For those that don't want to a quick listen to the song, here are the lyrics.
Oh, I learned a lesson
from the twentieth century
I don't think we should just dismiss
After one hundred years
of inhumanity
the lesson that I learned was this
Sometimes the solution
is worse than the problem
Let's stay together
Well I bought a ticket
to the revolution
and I cheered when the statues fell
Everyone came
to destroy what was wicked
but they killed off what was good as well
Sometimes the solution
is worse than the problem
Let's stay together
Stay with me
this century
Together we're better
Oh, I learned a lesson
from the twentieth century
It may be somewhat hit or miss
If you've certainty
'bout the way it's all meant to be
the lesson that you need is this
Sometimes the solution
is worse than the problem
Let's stay together
The song is about a plea to stay together rather than break-up with one's partner while using the lesson that the solution is worse than the problem obviously. Yet, it does make a good point about a lot of things that occurred in the 20th Century came from the solution to a previous problem. The line in the middle verse about revolution and "Everyone came to destroy what was wicked but they killed off what was good as well" is one that sticks in my brain from this song particularly with technological progress that can be good for an advancement of human progress yet can result in people losing a bit of their past as it causes changes in behavior.
So, that song is my go-to response for describing the 20th Century. Thinking about another way to sum it up just ended up as something that could be applied to any era of history. I was thinking something along the lines of: "Mankind contending with changes either self-created or by external forces and fighting those changes with or from advancing technology". To me, that encompasses things like the Bolshevik Revolution leading to Communist Russia and the fall-out from that, the two World Wars, the Depression dustbowl era, the Space Race, how cities are built and created, the rise of Fast Food but then fighting the effects of litter, waste or what effect that food can have on a person, the spreading and fighting of diseases from Spanish Flu to AIDS. Even stuff like movies, radio, tv, music were all affected by changes in technology and how to use it or stay relevant. With music, you're going from almost still classical at the start of the century to Jazz to Rock and Roll to EDM by the end.