Tumors are complex cellular and acellular environments within which cancer clones are under continuous selection pressures. Cancer cells are in a permanent mode of interaction and competition with each other as well as with the immediate microenvironment. In the course of these competitive interactions, cells share information regarding their general state of fitness, with less-fit cells being typically eliminated via apoptosis at the hands of those cells with greater cellular fitness. Competitive interactions involving exchange of cell fitness information have implications for tumor growth, metastasis, and therapy outcomes. Recent research has highlighted sophisticated pathways such as Flower, Hippo, Myc, and p53 signaling, which are employed by cancer cells and the surrounding microenvironment cells to achieve their evolutionary goals by means of cell competition mechanisms. In this review, we discuss these recent findings and explain their importance and role in evolution, growth, and treatment of cancer. We further consider potential physiological conditions, such as hypoxia and chemotherapy, that can function as selective pressures under which cell competition mechanisms may evolve differently or synergistically to confer oncogenic advantages to cancer.