In this talk, I will present a proof that the circle can be squared with pieces that have low Borel complexity and small dimension of boundary. The problem of circle-squaring dates back to Tarski in 1925. While the original proof uses the Axiom of Choice to produce an equidecomposition, Marks and Unger produced the first constructive proof in 2016 with Borel pieces, and Mathé, Noel, and Pikhurko improved this to Borel pieces with low complexity and small boundary in 2022. I will present the proof from the 2022 paper, with some modifications based on my work with Spencer Unger.