The object of the research is sandwich structures (beams and shells) under low-velocity and ballistic impact. The research is motivated by the widespread use of sandwich structures in various applications where they are subjected to impact loads. Method. The method involves an analytical approach using various models to calculate the deformation and failure of sandwich structures. Results. The specific results include detailed insights into the behavior of sandwich structures under different impact conditions. Notably, the study derives analytical models that depict the dynamic response, offering a comprehensive understanding of deflection and other key performance characteristics. In conclusion, this review consolidates current knowledge on the dynamic response of sandwich structures to low-velocity and ballistic impacts. The presented analytical models contribute valuable insights for optimizing the design of sandwich constructions in real-world applications.