The Old Order Amish (OOA) of Lancaster County Pennsylvania are a population isolate with a census size of ~35,000 individuals who descended from ~200 immigrants from Western Europe in the early 1700s. They have a long history of participation in genetic studies, for which their genealogical records and simple lifestyle offer substantial research advantages. However, their demographic history has altered their genomic landscape relative to their European counterparts. Knowledge of this landscape is critical to the design, execution, and interpretation of genetic studies in the OOA. In this dissertation, I evaluate the consequences of population bottleneck and genetic drift on the empirical and/or expected distribution of 1) linkage disequilibrium (LD) for common variants, 2) rare variation (with a focus on the implications for imputation accuracy using an external population) and 3) genomic estimates of inbreeding in the OOA.Using a high-density Single Nucleotide Polymorphism (SNP) map, I compare LD between OOA individuals and a reference population of European ancestry (HapMap CEU). For common SNPs (Minor Allele Frequency (MAF) ≥ 0.05), allele frequencies and LD profiles were similar between the OOA and CEU. Thus, public resources constructed from CEU data are appropriate for analyses of common genetic variation in the OOA.To assess the portability of deep sequencing resources, e.g., 1000 Genomes Project, for rare SNPs (MAF<0.05), I evaluate (via simulation and small-scale empirical study) the impact of using CEU versus OOA haplotype reference panels on imputation accuracy in the OOA. My results establish likely lower and upper bounds (0.50 and 0.75, respectively) of imputation accuracy for rare SNPs using 1000 Genomes Project-like resources in the OOA.Finally, using a subset of SNPs from the high-density map above, I estimate genomic inbreeding coefficients and compare them inbreeding conditional on the OOA pedigree, and describe the distribution of autozygous segments in the study participants. I observed strong agreement between genomic- and pedigree-based estimates, with a mean inbreeding coefficient of ~0.035, approximately the offspring of half 1st cousins. Furthermore, I establish that approximately 92% of the inbreeding in the OOA pedigree is due to inbreeding loops more distant than offspring of 2nd cousins.