Congenital cardiovascular malformations are the most common birth defects, with a complex multifactorial etiology. Genetic factors play an important role, illuminated by numerous cytogenetically visible abnormalities, as well as submicroscopic genomic imbalances affecting critical genomic regions in the affected individuals. Study of rare families with Mendelian forms, as well as emerging next-generation sequencing technologies have uncovered a multitude of genes relevant for human congenital cardiac diseases. It is clear that the complex embryology of human cardiac development, with an orchestrated interplay of transcription factors, chromatin regulators, and signal transduction pathway molecules can be easily perturbed by genomic imbalances affecting dosage-sensitive regions. This review focuses on chromosomal abnormalities contributing to congenital heart diseases and underscores several genomic disorders linked to human cardiac malformations in the last few decades.