There are two steps for any potential amendment. 1. proposal 2. ratification
And there are two ways for each. An amendment can be proposed by a constitutional convention (which can be called for by 2/3s of the state legislatures) or if it passes 2/3s of both houses of Congress. The amendment would then need to be ratified by 3/4s of the states (either through their own legislatures or state constitutional conventions). To date all amendments have been proposed by congress and ratified by state legislatures.
The high hurdle is why it doesn't happen so often. And in the modern eras highly polarized politics it is very unlikely that anything that is seen as partisan could get through the process.
The thing I think that has the greatest chance is electoral reform but only after the GOP loses a presidential election while winning the PV (ala Bush in 2000). A ban on the death penalty in a generation or two is possible if trends continue and it gains conservative support, but it may be more likely that such a ban would be enacted via legislation and/or the supreme court. In fact both the child labor and ERA are now seen as superfluous to current legislation and court rulings.
And if we are looking at the 21st century as a whole, one cannot ignore the possibility that technology may play a part, notably regarding the potential citizenship (or denial of citizenship) for human clones and/or artificial intelligences.
Actually the 21st amendment was ratified by state conventions rather than state legislatures. Congress thought that many state legislatures would be too conservative or too fearful of the temperance lobby to vote for a repeal of prohibition.
Anyway, most of the amendments that are currently talked about or supported by either party are long-shots to ever pass. The most likely thing I can think of might be DC statehood or just congressional representation. Maybe if we have a couple more 2000s in quick succession electoral college reform could be on the political radar. Talk of congressional term limits tends to sort of arise cyclically, so I imagine we'll hear serious debate about it again some day. Same with a balanced budget amendment.
