Borel circle squaring

In 1925 Alfred Tarski asked whether a square is equidecomposable by isometries with a disc of the same area. This question was answered in the affirmative in 1990 by Laczkovich. In 2015 Grabowski, Mathe and Pikhurko proved that one can require the pieces to be Lebesgue measurable or Baire measurable. In 2016 Marks and Unger further improved this theorem - they proved that they are equidecomposable using Borel pieces. We will discuss main ideas and tools used by Marks and Unger in their proof.