Myelodysplastic neoplasms (MDS) form a broad spectrum of clonal myeloid malignancies arising from hematopoietic stem cells that are characterized by progressive and refractory cytopenia and morphological dysplasia. Recent advances in unraveling the underlying pathogenesis of MDS have led to the identification of molecular drivers and secondary genetic events. With the overall goal of classifying patients into relevant disease entities that can aid to predict clinical outcomes and make therapeutic decisions, several MDS classification models (e.g., French–American–British, World Health Organization, and International Consensus Classification) as well as prognostication models (e.g., International Prognostic Scoring system (IPSS), the revised IPSS (IPSS-R), and the molecular IPSS (IPSS-M)), have been developed. The IPSS-M is the first model that incorporates molecular data for individual genes and facilitates better prediction of clinical outcome parameters compared to older versions of this model (i.e., overall survival, disease progression, and leukemia-free survival). Comprehensive classification and accurate risk prediction largely depend on the integration of genetic mutations that drive the disease, which is crucial to improve the diagnostic work-up, guide treatment decision making, and direct novel therapeutic options. In this review, we summarize the most common cytogenetic and genomic drivers of MDS and how they impact MDS prognosis and treatment decisions.