This chapter presents the basic theoretical results of fitting log-linear models by maximum likelihood. The level of mathematical sophistication is considerably higher than in the rest of the book. The presentation assumes knowledge of advanced calculus, mathematical statistics, and large sample theory. Although the results in this chapter are proven in a different manner than for regular linear models, the results themselves are quite similar in nature. The common linear structure of the two techniques leads to the well-known analogies between them. In fact, this chapter’s life began in the first edition of Christensen (Plane answers to complex questions: The theory of linear models (5th edn.). Springer (2020)) and assumes a knowledge of linear models at that level.