Integrable boundary interactions

I discuss some recent developments about integrable models of boundary interactions. I concentrate attention on the models having free massless (conformal) bulk dynamics, with the interaction solely due the nonlinear boundary conditions. I discuss relation between the boundary states of such models, innite sets of commuting local Integrals of Motion, and the Baxter's T- A nd Q-operators. I say few words about remarkable connection to ordinary differential equations, due to Dorey and Tateo. Although the meaning of this connection is yet to be understood, I present generalization suitable for exact solution of the so called "circular brane" model of boundary interaction, which has interesting applications in condensed matter theory.