Exosomes are small extracellular vesicles engaged in intercellular communication in both healthy and tumor cells. When released by the primary tumor, they transfer their cargo including nucleic acids, proteins, and lipids to target cells, thus modulating the character and fate of the recipient cells. By propagating their oncogenic content, exosomes are able to promote tumor progression, angiogenesis, metastases, and drug resistance. Their functions as delivery vehicles of biological material make exosomes promising biomarkers for the early prediction of disease progression and drug resistance in breast cancer, as well as for therapeutic targeting of molecules to treat this deadly disease. In the present review, we accentuate the relevance of exosomes as vehicles of prognostic and predictive markers and target molecules, and describe their potential therapeutic applications as drug cargo suppliers. We made an extensive literature research to clarify the association of their cargo, including exosomal DNA and RNA molecules, with the propagation of drug resistance.