Here's proof that your smartphone can "listen" to your conversations. Researchers proof of concept shows it can be done, and the evidence by some seems to indicate that something might already be doing that.

Some apps have to use the microphone, of course.

Time to go through all the apps to find out which ones use the microphone, and anything else i'm not keen on. I've not installed any apps that seem to have excessive, or unnecessary access requirements.

Many said they were discussing particular products or holiday destinations and shortly afterwards noticed advertising on the same theme. Your Smartphone Can Eavesdrop on Your Conversations [bbc.co.uk]

They created a prototype app, we started chatting in the vicinity of the phone it was on and watched our words appear on a laptop screen nearby.