Abstract: This is the first in a series of talks based on a recent paper of A.S. Marks and S.T. Unger. In 1925, Tarski asked if it is possible to decompose a disk in the plane into finitely many pieces and then rearrange them to form a square of the same area. Due to the apparent similarity between this problem and the Banach--Tarski paradox, it might appear that any such "circle squaring" must rely on the Axiom of Choice; and indeed, in 1990 Laczkovich answered Tarski's question in the affirmative using a non-constructive approach. However, Marks and Unger show in their paper that, somewhat surprisingly, it is possible to perform a "circle squaring" using only Borel pieces. In this talk I will go over the history of the problem and sketch some of the main ingredients that go into Marks and Unger's proof.