An Extensive Air Shower (EAS) is a cascade of ionized particles and photons produced in the atmosphere when a primary cosmic ray (CR) with energy higher than 10^{15} eV enters Earth atmosphere. Detection of EASs is an indirect, yet main observational method to study the energy, composition, and arrival directions of high energy CRs. Due to the stochastic nature of particle interactions involved in EAS, it can be studied only through vast numerical simulations based on Monte Carlo technique. In this talk, we will review observational and theoretical methods to study EASs and then discuss their roles in CR astrophysics.