Tissue engineering has been an inveterate area in the field of regenerative medicine for several decades. However, there remains limitations to engineer and regenerate tissues. Targeted therapies using cell-encapsulated hydrogels, such as mesenchymal stem cells (MSCs), are capable of reducing inflammation and increasing the regenerative potential in several tissues. In addition, the use of MSC-derived nano-scale secretions (i.e., exosomes) has been promising. Exosomes originate from the multivesicular division of cells and have high therapeutic potential, yet neither self-replicate nor cause auto-immune reactions to the host. To maintain their biological activity and allow a controlled release, these paracrine factors can be encapsulated in biomaterials. Among the different types of biomaterials in which exosome infusion is exploited, hydrogels have proven to be the most user-friendly, economical, and accessible material. In this paper, we highlight the importance of MSCs and MSC-derived exosomes in tissue engineering and the different biomaterial strategies used in fabricating exosome-based biomaterials, to facilitate hard and soft tissue engineering.