We discuss diffusion of particles in turbulent flows. In hydrodynamic turbulence, it is well known that distance between two particles imbedded in a turbulent flow exhibits a random walk behavior. The corresponding diffusion coefficient is ~ vinjlturb, where vinj is the amplitude of the turbulent velocity and lturb is the scale of the turbulent motions. It Is not clear whether or not we can use a similar expression for magnetohydrodynamic turbulence. However, numerical simulations show that mixing motions perpendicular to the local magnetic field are, up to high degree, hydrodynamical. This suggests that turbulent heat transport in magnetized turbulent fluid should be similar to that in non-magnetized one, which should have a diffusion coefficient ~ vinjlturb. We review numerical simulations that support this conclusion. The application of this idea to thermal conductivity in clusters of galaxies shows that this mechanism may dominate the diffusion of heat and may be efficient enough to prevent cooling flow formation when turbulence is vigorous.