Okay, so after searching on the web for some more, I found it: they moved it under "Touch ID & Passcode"
The details are outlined here.
To give you some more details:
When the phone is unlocked and you pull down the notification centre, you can swipe to the right to see the today summary and widgets (this applies to everyone). However, when the phone is locked, there was an option to display 1) nothing (you can't pull down the notification view), 2) today view only, 3) notification view only, or 4) both. This is different depending on how the user set up their phone.
I initially set up my phone such that only "notification view" would be accessible on the lock screen. This means that when my phone is locked and I pull down the notification centre, it will only show notification view, and I cannot swipe to the right to see the "today view". It looks like as though "today view" doesn't exist at all. But I wanted to change that, and I got confused because "notification centre" section was taken out altogether from Settings.
Anyhow, thanks for the help!