The clonal evolution (CE) model and the cancer stem cell (CSC) model are two independent models of cancers, yet recent data shows intersections between the two models. This article explores the impacts of the CSC model on the CE model. I show that CSC restriction, which depends on CSC frequency in cancer cell populations and on the probability of dedifferentiation of cancer non-stem cells (non-CSC) into CSCs, can favor or impede some patterns of evolution (linear or branched evolution) and some processes of evolution (drift, evolution by natural selection, complex adaptations). Taking CSC restriction into account for the CE model thus has implications for the way in which we understand the patterns and processes of evolution, and can also provide new leads for therapeutic interventions.