The relationships between cancer and stemness have a long history that is traced here. From the mid-19th century when the first theory on the embryonic origin of cancer was formulated to works on embryonal carcinoma cells in the mid-20th century, many steps have been crossed leading to the current cancer stem cell theory postulating that tumor growth is supported by a small fraction of the tumoral cells that have stem-like properties. However, in the last fifteen years, many works regularly encourage us to revise the concept of cancer stem cell. This article mentions key results that lead to a new perspective where cancer stem cells are primarily seen as cells exhibiting increased epigenetic plasticity and increased gene expression variability. This perspective suggests new therapeutical interventions consisting in stabilizing gene expression to control cancer cell proliferation and prevent stochastic gene expression variations that could lead to therapeutic resistance.