Echocardiographic measures of left ventricular remodeling, including left ventricular mass (LVM) and relative wall thickness (RWT), are powerful, independent predictors of heart disease morbidity and mortality. LVM and RWT are complex, quantitative traits influenced by genes, environment, and their interactions. The genetic architecture of complex traits is defined by the many loci from across the genome (in both candidate-genes and new genomic regions) operating independently, through gene-gene or gene-environment interactions. This dissertation aims to investigate the genetic architecture of LVM and RWT in the African-American population of the Genetic Epidemiology Network of Arteriopathy study. We first estimated the relative importance of genes in the variance of LVM and RWT (Chapter 2). The heritability of LVM and RWT after adjustment for risk factors was 0.416 (SE=0.07) and 0.235 (SE=0.07), respectively. Subsequently, we identified three single nucleotide polymorphisms (SNPs) from candidate-genes that exhibited significant internally replicated main effect associations with adjusted measures of LVM and one SNP associated with RWT (Chapter 3). Because of the potentially confounding effects of population substructure in genetic association studies, we explored the presence of substructure and identified admixture with a mean percent Caucasian ancestry of 16.5% (Chapter 4). Subsequent association analyses were adjusted for admixture using principal component analysis. Considering the interactions likely involved in complex traits, Chapter 5 examined 1,878 SNPs in 268 candidate-genes for main effects, SNP-environment, and SNP-SNP interactions associated with LVM. Based on three multiple testing criteria (False Discovery Rate, internal replication, and cross-validation), only 409 SNP-SNP interactions were considered significant. Finally, we conducted a genome-wide association study of 738,451 SNPs to identify new genomic regions associated with LVM or RWT (Chapter 6). After adjustment for known risk factors and population substructure, the strongest association was found for adjusted measures of LVM with a p-value=2.59x 10^-8 (rs12102921). The strongest signal for RWT was found at SNP rs1350003 with a p-value=2.18x10^-7. In an attempt to better understand the genetic architecture underlying inter-individual variation in LVM and RWT, this dissertation uses a variety of approaches to address methodological and statistical issues while highlighting the complexity of genetic effects associated with LVM and RWT.