A current high-priority phase of human genomics involves the development of a full Haplotype Map of the human genome [23]. It will be used in large-scale screens of populations to associate specific haplotypes with specific complex genetic-influenced diseases. A key, perhaps bottleneck, problem is to computationally infer haplotype pairs from genotype data. This paper follows the talk given at the DIMACS Conference on SNPs and Haplotypes held in November of 2002. It reviews several combinatorial approaches to the haplotype inference problem that we have investigated over the last several years. In addition, it updates some of the work presented earlier, and discusses the current state of our work.