Cancer is a collection of related genetic diseases exhibiting uncontrolled cell growth that interferes with normal functioning of human organisms. It results from accumulation of unfavorable mutations in tissues. While the biochemical picture of how cancer appears is known, the molecular mechanisms of tumor formation remain not fully understood despite tremendous efforts of researchers in multiple fields. New approaches for investigating cancer are constantly sought. In this paper, we discuss a powerful method of clarifying better a more microscopic picture of cancer by analyzing the dynamics of tumor formation. Using physics- and chemistry-inspired discrete-state stochastic description of cancer initiation, it is shown how the mechanisms of tumor formation can be uncovered. This approach is suggested as a powerful new physical-chemical tool for a better understanding of complex processes associated with cancer.