Birth defects are a leading cause of infant morbidity and mortality worldwide. The vast majority of birth defects are nonsyndromic, and although their etiologies remain mostly unknown, evidence supports the hypothesis that they result from the complex interaction of genetic, epigenetic, environmental, and lifestyle factors. Since our last review published in 2002 describing the basic tools of genetic epidemiology used to study nonsyndromic structural birth defects, many new approaches have become available and have been used with varying success. Through rapid advances in genomic technologies, investigators are now able to investigate large portions of the genome at a fraction of previous costs. With next-generation sequencing, research has progressed from assessing a small percentage of single-nucleotide polymorphisms to assessing the entire human protein-coding repertoire (exome)—an approach that is starting to uncover rare but informative mutations associated with nonsyndromic birth defects. Herein, we report on the current state of the genetic epidemiology of birth defects and comment on future challenges and opportunities. We consider issues of study design, and we discuss common variant approaches, including candidate gene studies and genome-wide association studies. We also discuss the complexities embedded in exploring interactions between genes and the environment. We complete our review by describing new and promising next-generation sequencing technologies and examining how the study of epigenetic mechanisms could become the key to unraveling the complex etiologies of nonsyndromic structural birth defects.