Fourier's Law of heat conduction describes diffusive heat transport in numerous real systems but is known to break down in one-dimensional (1D) systems. This implies that  the thermal conductivity of 1D systems diverges with  system size and energy transport is super-diffusive. In this talk, I will discuss approaches to understanding super-diffusive transport in different set-ups. I will first focus on understanding the differences in transport in integrable and non-integrable systems. Next I will  show how super-diffusive transport in specific analytically tractable stochastic non-integrable models can be described by thefractional diffusion equation (analogous to the heat equation for diffusive transport).