In 2001 Kadison proved a remarkable theorem which generalized the Pythagorean theorem in a new way. Together with the converse, called the Carpenter’s theorem, this gives a complete characterization of the diagonals of orthogonal projection matrices, that is, the sequences of numbers that can arise as the main diagonal of an orthogonal projection matrix. Amazingly, Kadison’s work also characterized the diagonals of projections on infinite dimensional Hilbert spaces. His work has sparked many researchers to study diagonals of operators in a number of diverse settings. In this talk we will see some of the recent work on diagonals of operators, as well as some surprising open problems.