It is well known that one can get the comparison theorems on their sample path for two diffusion processes in R¹ with same diffusion terms. In this talk, we will discuss the comparison problems for two diffusion processes with different diffusion terms. In general, we cannot obtain the comparison results on their sample path in this case. But we can get comparison results on their distributions and their convex order. Several comparison theorems are given for two uniformly elliptic diffusion processes and for two uniformly elliptic diffusion processes with jump. We also discuss the comparison problems for one kind of infinite dimensional diffusion, named supperdiffusion.