Myeloproliferative neoplasms are characterized by the acquisition at the hematopoietic stem cell level of driver mutations targeting the JAK/STAT pathway. In addition, they also often exhibit additional mutations targeting various pathways such as intracellular signalling, epigenetics, mRNA splicing or transcription. The natural history of myeloproliferative neoplasms is usually marked by a chronic phase of variable duration depending on the disease subtype, which can be followed by an accelerated phase or transformation towards more aggressive diseases such as myelofibrosis or acute leukemia. Besides, recent studies revealed important new information about the rates and mechanisms of sequential acquisition and selection of mutations in hematopoietic cells of myeloproliferative neoplasms. Better understanding of these events has been made possible in large part with the help of novel techniques that are now available to precisely decipher at the single cell level both the clonal architecture and the mutation-induced cell modifications. In this review, we will summarize the most recent knowledge about the mechanisms leading to clonal selection, how clonal architecture complexity can explain disease heterogeneity, and the impact of clonal evolution on clinical evolution.