This talk is concerned with Burgers equation with singular viscosity and singular flux. We realize that, when the singularity for flux is less than the singularity of viscosity, there exists smooth viscous shock wave, otherwise the shock wave does not exist. The main issue is to show the stability of these shock waves. To overcome the singularities caused by viscosity and flux, we use the weighted energy method, where the selection of weights are technical and play a crucial role in the proof. This talk is based on a series of studies joint with Dr. Xiaowen Li, Prof. Jingyu Li, Prof. Jean-Christophe Nave, Prof. Wancheng Sheng, and Dr. Shufang Xu.