Following conversations is so hard, one has to click around so many times.
Problem is that since then Twitter introduced this modified retweet that break said chains, and not every client do a good job of embedding what tweet people are replying to on sending etc.
On a completely different note, i see now that Twitter is trying to drum up attention for longer tweets. Something that is highly ironic given that over at SMS, where Twitter got its beginnings, stitching together multiple messages into a single long one has been a long solved "problem".
Edit: Back to the question at hand i think you will get a reasonable result with this:
And scroll downwards.
Doing a Google search for "twitter moments" results in the about page, again with no info on how to access the feature. This is followed by some news articles saying moments has been replaced by an "explore" tab, which I again can't find.
No wonder twitter is going down the drain. :-(
If you're signed in and don't see it perhaps when Moments first came out a couple years ago you installed one of the various addons to hide it and don't remember it?