While most SNP association studies are case-control based, family based designs and in particular case-parent trio designs have some very attractive features. We discuss and demonstrate those via a genome-wide and a candidate gene association study that employ case-parent trios. We also extend the logic regression methodology, originally developed for cohort and case-control studies, to detect SNP-SNP and SNP-environment interactions in studies of trios with affected probands. Trio logic regression accounts for the linkage disequilibrium (LD) structure in the genotype data, and accommodates missing genotypes via haplotype-based imputation. We also derive an efficient algorithm to simulate case-parent trios where genetic risk is determined via epistatic interactions.