Use this phrase to start a discussion about something that happened in the news or within your social circle. Here's an example of the second type:

Did you hear about Kylie getting engaged? I can't believe it!

You can use "Did you hear about ___" even if you strongly suspect that the listener has heard the news. But not if you know they've heard it.

When the news is someone's action, you use "someone doing something":

Did you hear about them getting arrested?

But you can also replace this part of the phrase with a noun:

Did you hear about the Nuclear Security Summit?