Eikonal equations arise in the fields of computer vision, image processing, geoscience, seismic tomography, to name a few. In some applications, the equation needs to be solved on a billion-point grid, and for tens of thousand times. In this talk, I will first introduce the most popular Fast Marching Method (FMM) by Sethian in 1996 and Fast Sweeping Method (FSM) by Zhao in 2005. Then I will briefly survey some modern variants and many parallelization techniques. In the last, I will describe a significant improvement when the algorithm is applied locally.