Static analysis aims at computing semantic properties of programs. Abstract interpretation provides a framework to design static analyses and allows one to divide the construction of a static analysis into the definition of abstract domains that describe families of logical predicates with operations to reason on them, and the semantic-guided formalisation of abstract interpreters. The latter relies on the abstract domains, that describe semantic properties, and on the concrete semantics. A large part of the research on static analysis focuses on the design of novel abstract domains, with ever more expressive and/or efficient computer representation for semantic properties. In this short paper, we consider more specifically the core of the abstract interpreters (also called the abstract iterators) and discuss several techniques to build them, that are inspired by functional programming. First, we briefly discuss common iteration techniques based on control flow graphs, which have often been used for program analyses aimed at computing state properties. Second, we consider iteration techniques that borrow principles from denotational semantics and are typically defined by induction over the syntax of programs. Last, we extend the latter family of techniques to relational abstractions that capture relations between program inputs and outputs.