This article surveys existing cohesive zone models (CZM) and their use in numerical simulations for analysis impacts on composite structures and predicting the damage induced. These models are used for matrix cracks and delamination. The first part of article gives the required background on failure criteria for predicting the onset of delaminations, on fracture mechanics and the various types of CZM. The second part discusses applications of CZM to several types of impact problems with composite structures. Applications for these models to other problems are briefly mentioned at the end. CZM are now part of state of the art numerical simulations with progressive damage analysis.