This chapter is concerned with maximum likelihood inference of discrete regression graph models. An optimization procedure is discussed based on a gradient-ascent algorithm to maximize the log-likelihood function where independence constraints are specified through Lagrange multipliers. The algorithm can be recursively applied to the sequence of multivariate regression models induced by the basic factorization of a regression graph. Model selection based on a structural learning of the DAG of the chain components is also discussed with reference to some illustrative applications.