In the end of the sixties, Shilnikov showed that the existence of a homoclinic orbit in a certain class of 3D flow implies the occurrence of chaotic behavior. This theorem was verified experimentally in glow-discharge systems, spiking neurons, rabbit arteries intermittency, electrochemical oscillators, among others. In the last two decades much work has been done to understand how the Shilnikov homoclinic orbits arise and are organized in the parameter space. In this talk, I will give an overview of this topic and present new results in the case of a 2-dimensional parameter space. I will also present numerical results of the Chua's circuit, where the prediction of the theory was verified.