Essential thrombocythemia (ET) is a Ph(-) myeloproliferative neoplasm characterized by elevated platelet counts. Patients most often have one of the three following driver mutations: JAK2, MPL, or CALR. However, these mutations are not detected in approximately 10–15% of patients, who are thus referred to as “triple-negative” (TN). Background/Objectives: In recent years, there have been breakthroughs in the genetic diagnosis of hematological diseases and progress in understanding their epigenetic basis. Aim: This study aimed to review the available literature and systematize the current knowledge on the molecular abnormalities in essential thrombocythemia. Particular attention was paid to the impacts of genetic mutations and epigenetic changes—such as abnormalities in non-coding RNA expression, DNA methylation, and histone modifications—on disease development and their clinical significance in patients with essential thrombocythemia. The most important publications on genetic and epigenetic mechanisms in essential thrombocythemia were reviewed and summarized. Methods: A review of the available literature was conducted using selected online databases. Publications from 2003 to 2026 were considered, covering the diagnosis and classification criteria for essential thrombocythemia, its genetic and epigenetic basis, and the associated impacts on the disease course. Conclusions: Although understanding the precise roles of genetic and epigenetic abnormalities in essential thrombocythemia remains challenging, they offer many opportunities for use as new diagnostic biomarkers and for the development of novel targeted treatment options. Further research is needed to better understand the genetic and epigenetic changes occurring in ET.