Item mappings are widely used in educational assessment for applications such as test administration (through test form assembly and computer assisted testing) and for criterion-referenced (CR) interpretation of test scores or scale anchoring. Item mappings are also used to construct ordered item booklets in the CTB/McGraw Hill Bookmark standard setting procedure. Selection rules for mapping the items vary with the purpose of the mapping. The objective of this paper is to categorize various types of item mappings, to describe ways to assess the consequences of a given item selection rule for mapping a binary item, and to provide a general empirical Bayes framework from which specific selection rules can be derived. A comparison is made on the maximum information (MI) rules and those derived from an empirical Bayes (EB) approach. It is noted that the EB rules coincide with the MI rules if the correction for guessing formula is used to extend the EB rules for Rasch and two parameter logistic items to the EB rules for three parameter logistic items. (Contains 13 references.) (Author/SLD)