The classical 2d chiral model is a conformally invariant field theory for which the fields are maps from a Riemann surface into a compact Lie group K, e.g. K=SU(2,C), and the classical solutions are harmonic maps. It is a longstanding problem to construct the corresponding quantum field theory. This model is believed to have a number of properties in common with 4d Yang-Mills gauge theory, such as (assuming K is simply connected) broken conformal invariance and asymptotic freedom, and there is a conjectural explicit scattering solution, hence the interest in the model. In this informal talk I will describe some of my ongoing attempts to construct the model.