Cancer is a complex disease resulting from the genetic and epigenetic disruption of normal cells. The mechanistic understanding of the pathways involved in tumor transformation has implicated a priori predominance of epigenetic perturbations and a posteriori genetic instability. In this work, we aimed to explain the mechanistic involvement of epigenetic pathways in the cancer process, as well as the abilities of natural bioactive compounds isolated from medicinal plants (flavonoids, phenolic acids, stilbenes, and ketones) to specifically target the epigenome of tumor cells. The molecular events leading to transformation, angiogenesis, and dissemination are often complex, stochastic, and take turns. On the other hand, the decisive advances in genomics, epigenomics, transcriptomics, and proteomics have allowed, in recent years, for the mechanistic decryption of the molecular pathways of the cancerization process. This could explain the possibility of specifically targeting this or that mechanism leading to cancerization. With the plasticity and flexibility of epigenetic modifications, some studies have started the pharmacological screening of natural substances against different epigenetic pathways (DNA methylation, histone acetylation, histone methylation, and chromatin remodeling) to restore the cellular memory lost during tumor transformation. These substances can inhibit DNMTs, modify chromatin remodeling, and adjust histone modifications in favor of pre-established cell identity by the differentiation program. Epidrugs are molecules that target the epigenome program and can therefore restore cell memory in cancerous diseases. Natural products isolated from medicinal plants such as flavonoids and phenolic acids have shown their ability to exhibit several actions on epigenetic modifiers, such as the inhibition of DNMT, HMT, and HAT. The mechanisms of these substances are specific and pleiotropic and can sometimes be stochastic, and their use as anticancer epidrugs is currently a remarkable avenue in the fight against human cancers.