We now have stemless glasses, but when and why did stemmed glassware become common? Does the stem keep the hand from warming the wine? Is the stem a handle, or does it serve only an aesthetic purpose?
A relevant answer here by /u/XenophontheAthenian addresses your question in part. Stemmed glasses are ancient in origin.
Yes, wineglasses have stems to keep your hand from warming the wine. This is especially important for white wine and sparkling wines like Champagne, which are served cold. This is also why in a fancy restaurant sparkling wines are served in buckets of ice, and served with a napkin or towel wrapped around the neck of the bottle, to keep the wine cold as it's poured. Stems also allow you to look at the wine in the light, which for red wine can be very beautiful and test the wine for "legs", when you tip the wineglass from one side to the other or swirl the wine around. You can see wine legs here, though the woman in the video is not using a stemmed glass. Stems keep the bowl of the glass clean from oily fingers, again to make the wine nicer to look at.