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The paper introduces Answer Set Programming with External Predicates (ASP-EX), a framework aimed at enabling ASP to deal with external sources of computation. This feature is realized by the introduction of “parametric” external predicates, whose extension is not specified by means of a logic program but computed through external code. With respect to existing approaches it is explicitly addressed the issue of invention of new information coming from external predicates, in form of new, and possibly infinite, constant symbols. Several decidable restrictions of the language are identified as well as suitable algorithms for evaluating Answer Set Programs with external predicates. The framework paves the way to Answer Set Programming in several directions such as pattern manipulation applications, as well as the possibility to exploit function symbols. ASP-EX has been successfully implemented in the DLV system, which is now enabled to make external program calls.