A and B branes from N=2 superspace

We present a manifestly supersymmetric description of A and B branes on Kaehler manifolds using a completely local N=2 superspace formulation of the world-sheet nonlinear sigma-model in the presence of a boundary. In particular, we show that an N=2 superspace description of type A boundaries is possible. This leads to a concrete realization of the still poorly understood coisotropic A branes. We also discuss briefly how the superspace description of a B brane provides an efficient way to compute higher loop beta-functions. In particular, we sketch how one obtains the fourth order derivative correction to the Born-Infeld action by using a beta-function method.