At a workshop it was suggested that it likely remains an open problem whether or not there is a 3- or 2 -piece dissection of a square to an equilateral triangle. Can anyone confirm that this is unresolved?

Four-piece dissections are known, the most famous being Henry Dudeney's century-old gem:
http://cs.smith.edu/~orourke/MathOverflow/Dudeney.gif http://cs.smith.edu/~orourke/MathOverflow/DissectionFixed.gif
                _{[Maple animation from this link.]}

And here is a 5-piece dissection.