I will introduce the definition of contact homology proposed by Eliashberg, Hofer, and Givental in 2000. Then we will see that this definition does not work, because the moduli spaces of $J$-holomorphic curves that we count to define the differential of contact homology are not transversally cut out. In order to achieve transversality, we will use a Semi-global Kuranishi structure, a simplified version of the Fukaya-Oh-Ono-Ohta's Kuranishi structure, to perturb the moduli space of $J$-holomorphic curves. If time permits, I will also explain the application of Semi-Kuranishi structures to define equivariant Lagrangian Floer homology. This is a joint work with Ko Honda.