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Recent advances in the foundations and the implementations of functional logic programming languages originate from far-reaching results on narrowing evaluation strategies. Narrowing is a computation similar to rewriting which yields substitutions in addition to normal forms. In functional logic programming, the classes of rewrite systems to which narrowing is applied are, for the most part, subclasses of the constructor-based, possibly conditional, rewrite systems. Many interesting narrowing strategies, particularly for the smallest subclasses of the constructor-based rewrite systems, are generalizations of well-known rewrite strategies. However, some strategies for larger non-confluent subclasses have been developed just for functional logic computations. This paper discusses the elements that play a relevant role in evaluation strategies for functional logic computations, describes some important classes of rewrite systems that model functional logic programs, shows examples of the differences in expressiveness provided by these classes, and reviews the characteristics of narrowing strategies proposed for each class of rewrite systems.