A Baxter algebra is an algebra with a operator that satisfies the Baxter identity

for a constant lambda. It is also known as Rota-Baxter algebras to the physicists. Studied in early years by Baxter, Cartier and Rota, Baxter algebras have recently been related to Hopf algebras, operad theory, combinatorics and math physics. We will describe two applications in number theory. The first is in generating functions of numbers such as Stirling numbers and multi-nomial coefficients. The second is in multiple zeta values.