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Boolean satisfiability (SAT) finds a wide range of practical applications, including Artificial Intelligence and, more recently, Bioinformatics. Although encoding some combinatorial problems using Boolean logic may not be the most intuitive solution, the efficiency of state-of-the-art SAT solvers often makes it worthwhile to consider encoding a problem to SAT. One representative application of SAT in Bioinformatics is haplotype inference. The problem of haplotype inference under the assumption of pure parsimony consists in finding the smallest number of haplotypes that explains a given set of genotypes. The original formulations for solving the problem of Haplotype Inference by Pure Parsimony (HIPP) were based on Integer Linear Programming. More recently, solutions based on SAT have been shown to be remarkably more efficient. This paper provides an overview of SAT-based approaches for solving the HIPP problem and identifies current research directions.