Oncological diseases have always been among the most significant pathologies. Therefore, development of effective antitumor drugs is considered one of the priorities of modern healthcare. Inhibitors of proteins, enzymes, and receptors that regulate the signaling pathways of tumor cells, as well as apoptosis inductors, are used for tumor chemotherapy. The most significant and studied signaling pathways are the Raf/MEK/ERK and phosphoinositide-3 kinase (PI3K). Changes in the cascades of these pathways lead to the modulation of many cellular functions, such as cell growth and survival, proliferation, differentiation, and adhesion. These signaling cascades are closely related to Ras proteins. Oncogenic forms of Ras proteins are detected in a large number of tumor diseases—more than 30% of all forms of neoplasms. The literature data of the last 30 years on the study of the key stages of signaling cascades initiated by oncogenic Ras proteins are considered in this review. The processing features of Ras proteins, which are currently considered as promising molecular targets for the development of antitumor drugs, are analyzed separately. Literature data on new strategies to search for effective antineoplastic agents, which are based on Ras proteins signaling pathways, and bipharmacophore compounds are presented and discussed.