My DS is 2.4yo and is just starting to get the hang of the animal in shapes type of puzzle. He fits them in by first fitting a paw or a tail whereas he was just randomly plugging away at the shapes. He doesn't yet do what we do: look at the whole shape and fit it in. He'll do 2-piece puzzles if the colours are obvious and the fit is easy but can't do 3- or 4-piece ones. He's figured out shape-sorters now (wasn't doing it at 2y checkup).
What are yours doing? I'm just interested in the range at this age.