In aerospace engineering applications, lightweight material structures are considered to perform difficult service conditions and afford energy efficiency. Therefore, composite materials have gained popularity due to their light weights and high performances in structural design. Mechanical loads and environmental conditions primarily create damage to structural materials, thus numerous studies have considered the repair of the damaged structure. Bonded composite repairs are generally chosen, as they provide enhanced stress-transfer mechanisms and joint efficiencies with the increased use of advanced composite materials in primary and secondary aircraft structural components. Thus, it is essential to have reliable and repeatable bonded repair procedures to restore damaged structural components. However, composite bonded repairs, especially with primary structures, present several scientific challenges in the current existing repair technologies. In this review, a study has been done on the bonded composite repair of damaged structures with the stress-intensity factor (SIF) as the parameter for defining the extent of failure by composite repair and unrepaired material structures. In this work, various types of repair methods and the techniques used by researchers are critically reviewed, and future opportunities are explored. The present study was limited to the composite and aluminium materials that are common in aerospace applications.