In this paper, we present a survey of the approximability and fixed-parameter tractability results for some Exemplar Genomic Distance problems. We mainly focus on three problems: the exemplar breakpoint distance problem and its complement (i.e., the exemplar non-breaking similarity or the exemplar adjacency number problem), and the maximal strip recovery (MSR) problem. The following results hold for the simplest case between only two genomes (genomic maps) G and H, each containing only one sequence of genes (gene markers), possibly with repetitions.