Application of traditional somatic evolutionary theory can offer an appropriate context for studying tumor growth at the molecular level. However, high degrees of heterogeneity (especially genome-level heterogeneity) within tumors coupled with a lack of common driver mutations have posed a challenge to the generally accepted stepwise concept of cancer evolution, where clonal expansion is the key. In order to account for multiple levels of heterogeneity and better understand tumor growth and progression, a new, holistic conceptual framework must be applied in cancer research. Herein, we discuss one such framework, the genome theory of cancer evolution, with respect to tumor growth. This includes detailing the ultimate importance of chromosome aberrations in cancer, the somatic cell evolutionary pattern, and single-cell/population growth dynamics. Under this new framework, tumor growth is a highly dynamic process where emergent outlier subpopulations can greatly influence the pattern of progression and the direction of evolution. Further, genome level changes have a greater impact on cancer evolution than individual gene mutations in most cancer types, as karyotype alteration often results in altered system inheritance which defines the network structure and even can change the meaning of individual genes (representing 'parts inheritance' by changing the gene context. Based on this analysis, we call for a focus shift back on cytogenetic and cytogenomic alterations (especially on non-clonal chromosomal aberrations) in monitoring population growth, identifying the emergence of new subpopulations and studying patterns of evolutionary dynamics. This new insight has implications in understanding cancer evolution in general as well as searching for new diagnostic and treatment strategies.