Myeloid neoplasms encompass a very heterogeneous family of diseases characterized by the failure of the molecular mechanisms that ensure a balanced equilibrium between hematopoietic stem cells (HSCs) self-renewal and the proper production of differentiated cells. The origin of the driver mutations leading to preleukemia can be traced back to HSC/progenitor cells. Many properties typical to normal HSCs are exploited by leukemic stem cells (LSCs) to their advantage, leading to the emergence of a clonal population that can eventually progress to leukemia with variable latency and evolution. In fact, different subclones might in turn develop from the original malignant clone through accumulation of additional mutations, increasing their competitive fitness. This process ultimately leads to a complex cancer architecture where a mosaic of cellular clones—each carrying a unique set of mutations—coexists. The repertoire of genes whose mutations contribute to the progression toward leukemogenesis is broad. It encompasses genes involved in different cellular processes, including transcriptional regulation, epigenetics (DNA and histones modifications), DNA damage signaling and repair, chromosome segregation and replication (cohesin complex), RNA splicing, and signal transduction. Among these many players, transcription factors, RNA splicing proteins, and deubiquitinating enzymes are emerging as potential targets for therapeutic intervention.