Composite materials are known to have a poor resistance to through-the-thickness impact loading. There are various methods for improving their impact damage tolerance, such as fiber toughening, matrix toughening, interface toughening, through-the-thickness reinforcements, and selective interlayers and hybrids. Hybrid composites with improved impact resistance are particularly useful in military and commercial civil applications. Hybridizing composites using shape memory alloys (SMA) is one solution since SMA materials can absorb the energy of the impact through superelastic deformation or recovery stress, reducing the effects of the impact on the composite structure. The SMA material may be embedded in the hybrid composites (SMAHC) in many different forms and also the characteristics of the fiber reinforcements may vary, such as SMA wires in woven laminates or SMA foils in unidirectional laminates, only to cite two examples. We will review the state of the art of SMAHC for the purpose of damage suppression. Both the active and passive damage suppression mechanisms will be considered.