(1) Introduction: Extrapyramidal disorders form the so-called extrapyramidal syndrome (EPS), which is characterized by the occurrence of motor disorders as a result of damage to the basal ganglia and the subcortical-thalamic connections. Often, this syndrome develops while taking medications, in particular antipsychotics (APs). (2) Purpose: To review studies of candidate genes encoding dopamine receptors as genetic predictors of development of AP-induced parkinsonism (AIP) and AP-induced tardive dyskinesia (AITD) in patients with schizophrenia. (3) Materials and Methods: A search was carried out for publications of PubMed, Web of Science, Springer, and e-Library databases by keywords and their combinations over the last 10 years. In addition, the review includes earlier publications of historical interest. Despite extensive searches of these commonly used databases and search terms, it cannot be ruled out that some publications were possibly missed. (4) Results: The review considers candidate genes encoding dopamine receptors involved in pharmacodynamics, including genes DRD1, DRD2, DRD3, and DRD4. We analyzed 18 genome-wide studies examining 37 genetic variations, including single nucleotide variants (SNVs)/polymorphisms of four candidate genes involved in the development of AIP and AITD in patients with schizophrenia. Among such a set of obtained results, only 14 positive associations were revealed: rs1799732 (141CIns/Del), rs1800497 (C/T), rs6275 (C/T), rs6275 (C/T) DRD2; rs167771 (G/A) DRD3 with AIP and rs4532 (A/G) DRD1, rs6277 (C/T), rs6275 (C/T), rs1800497 (C/T), rs1079597 (A/G), rs1799732 (141CIns/Del), rs1045280 (C/G) DRD2, rs6280 (C/T), rs905568 (C/G) DRD3 with AITD. However, at present, it should be recognized that there is no final or unique decision on the leading role of any particular SNVs/polymorphisms in the development of AIP and AITD. (5) Conclusion: Disclosure of genetic predictors of the development of AIP and AITD, as the most common neurological adverse drug reactions (ADRs) in the treatment of patients with psychiatric disorders, may provide a key to the development of a strategy for personalized prevention and treatment of the considered complication of AP therapy for schizophrenia in real clinical practice.