Intratumor heterogeneity inherent in the majority of human cancers is a major obstacle for a highly efficient diagnosis and successful prognosis and treatment of these diseases. Being a result of clonal diversity within the same tumor, intratumor heterogeneity can be manifested in variability of genetic and epigenetic status, gene and protein expression, morphological structure, and other features of the tumor. It is most likely that the appearance of this diversity is a source for the adaptation of the tumor to changes in microenvironmental conditions and/or a tool for changing its malignant potential. In any case, both processes result in the appearance of cell clones with different undetermined sets of hallmarks. In this review, we describe the heterogeneity of molecular disorders in various human tumors and consider modern viewpoints of its development including genetic and non-genetic factors of heterogeneity origin and the role of cancer stem cells and clonal evolution. We also systematize data on the contribution of tumor diversity to progression of various tumors and the efficiency of their treatment. The main problems are indicated in the diagnosis and therapy of malignant tumors caused by intratumor heterogeneity and possible pathways for their solution. Moreover, we also suggest the key goals whose achievement promises to minimize the problem of intratumor heterogeneity and to identify new prognostic, predictive, and target markers for adequate and effective treatment of cancer.