Statistical approaches used for gene mapping can be divided into two types: linkage and association analysis. This dissertation work addresses statistical methods in both areas.In the area of linkage analysis, I consider the problem of QTL (Quantitative Trait Locus) linkage analysis. Linkage analysis requires family data, and if the families are selected according to phenotype or if the trait of interest has a non-Gaussian distribution, standard analysis methods may be inappropriate. The score statistic, derived by taking the first derivative of the likelihood with respect to the linkage parameter, maintains the power of likelihood-based methods and with the use of an empirical variance estimator is robust against non-normal traits and selected samples. I investigate a number of empirical variance estimators that can be used for general pedigrees and evaluate the effects of different variance estimators and trait parameter estimates on the power of the score statistic.In the area of association analysis, I consider the question of what is the best model for a simple genome-scan analysis of a case-control study. In a case-control genome-wide association study, hundreds of thousands of SNPs are genotyped and statistical analysis usually starts with 1 or 2 df chi-squared test or logistic regression model. Power comparisons among subsets of these methods have been done but none of these papers have comprehensively tackled the question of which method is best for univariate scanning in a genome scan. I compare different test procedures and regression models for case-control studies starting from single-locus analysis followed by scanning with covariates and then genome-wide analysis. Based on the simulation results, I offer guidelines for choosing robust test procedures or regression models for testing the genetic effect.The methods proposed here can be used to improve the efficiency of gene mapping studies. This will lead to quicker and more reliable discoveries of genetic risk factors for many different diseases with great public health importance, which should in turn lead to improved prevention and treatment strategies.