Cell death is an innate capability of cells to be removed from microenvironment, if and when they are damaged by multiple stresses. Cell death is often regulated by multiple molecular pathways and mechanism, including apoptosis, autophagy, and necroptosis. The molecular network underlying these processes is often intertwined and one pathway can dynamically shift to another one acquiring certain protein components, in particular upon treatment with various drugs. The strategy to treat human cancer ultimately relies on the ability of anticancer therapeutics to induce tumor-specific cell death, while leaving normal adjacent cells undamaged. However, tumor cells often develop the resistance to the drug-induced cell death, thus representing a great challenge for the anticancer approaches. Numerous compounds originated from the natural sources and biopharmaceutical industries are applied today in clinics showing advantageous results. However, some exhibit serious toxic side effects. Thus, novel effective therapeutic approaches in treating cancers are continued to be developed. Natural compounds with anticancer activity have gained a great interest among researchers and clinicians alike since they have shown more favorable safety and efficacy then the synthetic marketed drugs. Numerous studies in vitro and in vivo have found that several natural compounds display promising anticancer potentials. This review underlines certain information regarding the role of natural compounds from plants, microorganisms and sea life forms, which are able to induce non-apoptotic cell death in tumor cells, namely autophagy and necroptosis.