The success of genomic selection programs in dairy cattle populations has resulted in a growing demand for new methods to increase the accuracies of genomic estimated breeding values ( GEBV ) and to calculate more precisely inbreeding coefficient. The main objectives of this thesis were 1) to investigate the accuracy and bias of GEBV using genomic best linear unbiased prediction ( GBLUP ) with alternate genomic relationship matrices ( G ) based on single nucleotide polymorphism () and haplotypes information in simulated and real data (first study), and 2) to determine the optimal method for estimating true inbreeding based on simulated data, and to characterize the distribution of runs of homozygosity ( ROH ) across the genome of real and simulated populations (second study). In the first study, alternate G matrices were constructed for simulated populations for two traits with heritability of 0.3 and 0.1. In addition, genomic relationship matrices were built using actual 50k chip genotypes and fat yield, milk yield, somatic cell score, conformation, and days open were analyzed in the North American Holstein cattle. In the second study, a gene dropping simulation was performed and inbreeding estimates based on ROH, pedigree, and the genomic relationship matrix were compared to true inbreeding. Furthermore, inbreeding coefficients were estimated in a sample of genotyped North American Holstein animals born from 1990 to 2016 using 50k chip data and ROH patterns were assessed before and after genomic selection. Based on the results of the first study, the use of haplotype relationship matrixes ( G HAP ) yielded slightly higher prediction accuracy than other matrices, in simulation. Using LD-haploblocks based relationship matrix ( G HAP-LD ) compare to use of G HAP did not result in more accurate estimates. Constructing haplotype-based relationship matrices based on giving credit to long haplotype ( G HAP2 ) did not result in more accurate GEBVs. Results of the second study revealed that using ROH with a minimum window size of 20 to 50 (1 to 2.5Mb) using 1101 software provides the closest estimates to true inbreeding in simulation study. Pedigree inbreeding tended to underestimate true inbreeding, and results for genomic inbreeding varied depending on assumptions about base allele frequencies. The longest individual ROH and the largest average length of ROH were observed when selection was based on best linear unbiased prediction ( BLUP ), whereas genomic selection showed the largest number of small ROH compared to BLUP estimated breeding values ( BLUP-EBV ). In North American Holsteins, the average number of ROH segments of 1 Mb or more per individual increased from 57 in 1990 to 82 in 2016. Based on current results, G HAP might be an alternative approach to reduce bias of genomic predictions in routine genomic evaluations. Genomic selection based on G HAP instead of G improved genomic predictions slightly especially for low heritable traits under recent selection, such as days open. Furthermore, this study shows that ROH based approach can accurately identify autozygosity across the genome, provided appropriate threshold parameters are used. Our results show how different selection strategies affect the distribution of ROH, and how the distribution of ROH has changed in the North American dairy cattle population over the last 25 years. Key words: Accuracy, Bias of prediction, Genomic relationship matrix, Haplotype, Inbreeding, Real data, ROH, Simulation