Azadirachta indica, also known as neem, is commonly found in many semi-tropical and tropical countries including India, Pakistan, and Bangladesh. The components extracted from neem plant have been used in traditional medicine for the cure of multiple diseases including cancer for centuries. The extracts of seeds, leaves, flowers, and fruits of neem have consistently shown chemopreventive and antitumor effects in different types of cancer. Azadirachtin and nimbolide are among the few bioactive components in neem that have been studied extensively, but research on a great number of additional bioactive components is warranted. The key anticancer effects of neem components on malignant cells include inhibition of cell proliferation, induction of cell death, suppression of cancer angiogenesis, restoration of cellular reduction/oxidation (redox) balance, and enhancement of the host immune responses against tumor cells. While the underlying mechanisms of these effects are mostly unclear, the suppression of NF-κB signaling pathway is, at least partially, involved in the anticancer functions of neem components. Importantly, the anti-proliferative and apoptosis-inducing effects of neem components are tumor selective as the effects on normal cells are significantly weaker. In addition, neem extracts sensitize cancer cells to immunotherapy and radiotherapy, and enhance the efficacy of certain cancer chemotherapeutic agents. This review summarizes the current updates on the anticancer effects of neem components and their possible impact on managing cancer incidence and treatment.