Exosomes are nanosized vesicles that are produced in normal and cancer cells, promoting intracellular communication. In head and neck cancer (HNC), exosomes are involved in many undesirable events of cancer development and progression, including angiogenesis, tumor microenvironment (TME) remodeling, invasion, epithelial-to-mesenchymal transition (EMT), metastasis, extracellular matrix (ECM) degradation, and drug resistance. Exosomes are involved in altering the signaling pathways in recipient cells by the cargoes they carry. Proteins, lipids, and nucleic acids such as DNA fragments and RNAs (i.e., mRNAs, miRNAs, and long non-coding RNAs) are carried in the exosomes to promote cell communication. EMT is a critical cellular process in which epithelial cells are forced to become mesenchymal cells by the actions of SNAIL/SLUG, TWIST, and ZEB family transcription factors carried in exosomes that facilitate metastasis. In this critical review, we focused on exosome biogenesis, their cargoes, and their involvement in EMT induction and metastasis during HNC. Insights into exosome isolation and characterization, as well as their key role in ECM remodeling and degradation, are also presented and critically discussed. More importantly, this article addresses the role of exosomes in HNC and drug resistance induced in drug-sensitive cancer cells. In addition, exosomes have a great potential to be used as diagnostic and therapeutic tools. A better understanding on exosome biogenesis, composition, and functions in HNC will aid in developing novel therapeutic strategies to treat HNC, overcome therapy resistance, and avoid metastasis, which is a significant cause of cancer death.