Foam is a fluid that consists of water, gas, and surfactant, so that its properties are a combination of the two. Water-soluble surfactant is used to stabilize the fluid. From the late 50s and early 60s, foam as a promising technique to control gas mobility and adaptability to porous media, as well as solving problems such as finger phenomenon, early gas breakthrough, gravity override, etc. that are created by gas injection are presented. Applications of foam injection including: EOR, matrix acidizing, prevention of gas leakage, repair of aquifer layers, closing the path in the porous medium in order to control the flow and direct it. To understand the physicality of this fluid, it has been modeled in the past with two general techniques of population balance and local equilibrium. In this article, these approaches and models are explained. Also, a general comparison has been made between the presented techniques. The population balance pattern, which is based on the rules of bubble balance, is classified into two versions: 1-dynamic texture and 2-local equilibrium. The main difference between the two versions is in how to obtain the foam texture. The results show that the local-implicit texture equilibrium technique requires fewer parameters than the population balance model versions. Also, due to the algebraic solution of equations, it takes less computational time in reservoir simulators and is more useful due to its experimental nature.