Hypertension is one of the strongest modifiable cardiovascular risk factors, affecting an increasing number of people worldwide. Apart from poor medication adherence, the low efficacy of some therapies could also be related to inter-individual genetic variability. Genetic studies of families revealed that heritability accounts for 30% to 50% of inter-individual variation in blood pressure (BP). Genetic factors not only affect blood pressure (BP) elevation but also contribute to inter-individual variability in response to antihypertensive treatment. This article reviews the recent pharmacogenomics literature concerning the key classes of antihypertensive drugs currently in use (i.e., diuretics, β-blockers, ACE inhibitors, ARB, and CCB). Due to the numerous studies on this topic and the sometimes-contradictory results within them, the presented data are limited to several selected SNPs that alter drug response. Genetic polymorphisms can influence drug responses through genes engaged in the pathogenesis of hypertension that are able to modify the effects of drugs, modifications in drug–gene mechanistic interactions, polymorphisms within drug-metabolizing enzymes, genes related to drug transporters, and genes participating in complex cascades and metabolic reactions. The results of numerous studies confirm that genotype-based antihypertension therapies are the most effective and may help to avoid the occurrence of major adverse events, as well as decrease the costs of treatment. However, the genetic heritability of drug response phenotypes seems to remain hidden in multigenic and multifactorial complex traits. Therefore, further studies are required to analyze all associations and formulate final genome-based treatment recommendations.