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Every sixth death in the world is due to cancer, making it the second leading cause of death. Around one-third of deaths from cancer are due to tobacco use, high body mass index, alcohol use, low fruit and vegetable intake, and lack of physical activity. Anticancer drugs are those which are used to cure malignant disease i.e., Cancer. Topological indices are used to model physico-chemical properties and biological activities of chemical compounds. In this paper, we compute \textit{$M$-polynomial} and \textit{$NM$-polynomial} of anticancer drugs. Further, we retrieve some degree and neighborhood degree based topological indices of anticancer drugs from their respective \textit{$M$-polynomial} and $NM$-polynomial. The theoretical results obtained in this article have promising aspects in designing novel drug for the treatment of Cancer.