Congenital heart defects (CHD) are the most common congenital abnormality, with an overall global birth prevalence of 9.41 per 1000 live births. The etiology of CHDs is complex and still poorly understood. Environmental factors account for about 10% of all cases, while the rest are likely explained by a genetic component that is still under intense research. Transcription factors and signaling molecules are promising candidates for studies regarding the genetic burden of CHDs. The present narrative review provides an overview of the current knowledge regarding some of the genetic mechanisms involved in the embryological development of the cardiovascular system. In addition, we reviewed the association between the genetic variation in transcription factors and signaling molecules involved in heart development, including TBX5, GATA4, NKX2-5 and CRELD1, and congenital heart defects, providing insight into the complex pathogenesis of this heterogeneous group of diseases. Further research is needed in order to uncover their downstream targets and the complex network of interactions with non-genetic risk factors for a better molecular–phenotype correlation.