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.