Milne, J.S., The points on a Shimura variety modulo a prime of good reduction. In: The Zeta Function of Picard Modular Surfaces, Publ. Centre de Rech. Math., Montreal (Eds. R. Langlands and D. Ramakrishnan), 1992, pp. 151--253.except that the TeX has been updated, some corrections and minor editorial changes made, and some footnotes added. Significant changes to the original article have been noted in footnotes.
We explain, in the case of good reduction, the conjecture of Langlands and Rapoport (1987) describing the structure of the points on the reduction of a Shimura variety, and we derive from it the formula conjectured by Kottwitz (1990) expressing a certain trace as a sum of products of (twisted) orbital integrals. Also we introduce the notion of an integral canonical model for a Shimura variety, and we extend the conjecture of Langlands and Rapoport to Shimura varieties defined by groups whose derived group is not simply connected. Finally, we briefly review Kottwitz's stabilization of his formula.