The reflection equation algebra is a quantization of the ring of functions on $n \times n$ matrices. Reshetikhin gave a diagrammatic description of a set of algebraically independent generators of the center. I will describe joint work with David Jordan giving explicit algebraic formulas for Reshetikhin’s generators and establishing quantum Newton and Cayley–Hamilton identities for them. An important special case is the quantum determinant, for which an explicit algebraic formula was previously only known when $n = 2$. As an immediate corollary we obtain an algebraically independent set of generators for the center of the Drinfeld–Jimbo quantum group. Our approach unifies the descriptions of the center given by Reshetikhin, by Nazarov–Tarasov, and by Gurevich–Pyatov–Saponov.