A very effective way to approximate partial differential equations (PDEs) is to use radial basis functions (RBFs). To solve PDEs, many RBF method types are presented in this study. RBF methods are widely used to solve PDEs because of their mesh-free nature, simplicity of use, and independence from dimension. The Kansa method, the Hermite symmetric approach, the localized method, and the hybrid method are some of the generalized RBF approaches we study in this paper. We also talked about how mesh-free solutions like RBF are preferred over mesh-based ones. Also mentioned is a recent advancement in RBF approximation for PDE solution. For better comprehension, the mathematical formulation of various RBF algorithms is discussed. Because they can reach spectral accuracy even with unstructured node topologies, radial basis functions (RBFs) are gaining a lot of attention as a technique for solving PDEs. Such node sets offer chances for local node customization as well as geometric flexibility. The RBF generated finite difference (RBF-FD approaches can offer significant savings in computer resources (time and memory), although requiring a slightly higher overall number of nodes for the same accuracy.