Head and neck squamous cell carcinoma (HNSCC) is one of the most fatal cancers worldwide. Despite advances in the management of HNSCC, the overall survival for patients has not improved significantly due to advanced stages at diagnosis, high recurrence rate after surgical removal, and second primary tumor development, which underscore the importance of novel strategies for cancer prevention. Cancer chemoprevention, the use of natural or synthetic compounds to prevent, arrest, or reverse the process of carcinogenesis at its earliest stages, aims to reverse premalignancies and prevent second primary tumors. Genomics and proteomics information including initial mutation, cancer promotion, progression, and susceptibility has brought molecularly targeted therapies for drug development. The development of preventive approaches using specific natural or synthetic compounds, or both, requires a depth of understanding of the cross-talk between cancer signaling pathways and networks to retain or enhance chemopreventive activity while reducing known toxic effects. Many natural dietary compounds have been identified with multiple molecular targets, effective in the prevention and treatment of cancer. This review describes recent advances in the understanding of the complex signaling networks driving cancer progression and of molecularly targeted natural compounds under preclinical and clinical investigation.