Recent research has dramatically advanced our understanding of the genetic basis of multiple myeloma (MM). MM displays enormous inter- and intratumoral heterogeneity, and underlies a clonal evolutionary process driven and shaped by diverse factors such as clonal competition, tumor microenvironment, host immunity, and therapy. Two main cytogenetic groups are distinguished: MM with recurrent translocations involving the immunoglobulin heavy chain locus and MM with hyperdiploidy involving the odd chromosomes. The disease virtually always starts with a preneoplastic prodromal phase-monoclonal gammopathy of undetermined significance-that variably progresses to symptomatic MM within a few months or many years. Tumor heterogeneity and its evolution in space and time have important consequences for the clinical management and outcome of MM patients. At diagnosis, spatial intratumoral heterogeneity poses a challenge for classification and risk stratification. During maintenance therapy, clonal evolution may complicate disease monitoring and promote drug resistance. Upon progression or transformation, identifying the dominant disease-driving neoplastic clones and elucidating their properties are key to tailor personalized therapy. In this review, we discuss tumor heterogeneity and clonal evolution in MM, integrating pathological, radiological, molecular genetics, and clinical data. Current and prospective classification schemes and prognostic parameters, incorporating new genetic and proteomic discoveries and advances in imaging, are highlighted. In addition, the roles of the tumor microenvironment, host immunity, and resistance mutations, and their effects on therapy, are discussed. An improved understanding of high-risk disease, tumor heterogeneity, and clonal evolution will guide future therapies and may ultimately lead towards a cure for MM.