The genomic landscape of head and neck squamous cell carcinoma (HNSCC) has been recently elucidated. Key epigenetic and genetic characteristics of this cancer have been reported and substantiated in multiple data sets, including those distinctive to the growing subset of human papilloma virus (HPV)-associated tumors. This increased understanding of the molecular underpinnings of HNSCC has not resulted in new approaches to treatment. Three Food and Drug Administration-approved molecular targeting agents are currently available to treat recurrent/metastatic disease, but these have exhibited efficacy only in subsets of HNSCC patients, and thus surgery, chemotherapy, and/or radiation remain as standard approaches. The lack of predictive biomarkers to any therapy represents an obstacle to achieving the promise of precision medicine. This review aims to familiarize the reader with current insights into the HNSCC genomic landscape, discuss the currently approved and promising molecular targeting agents under exploration in laboratories and clinics, and consider precision medicine approaches to HNSCC.