Areal density increases in conventional perpendicular magnetic recording are becoming increasingly difficult to achieve. Heat assisted magnetic recording is viewed as a potential technique to extend magnetic recording into the multiple-terabit range. Over the last 5 years, we have performed extensive simulations of Heat Assisted Magnetic Recording on both granular and bit-patterned media. For this purpose, we represent  the behavior of granular media near the Curie temperature with renormalized blocks of spins of order 1 nm3. The change in magnetization of these blocks can then be evaluated using the Landau-Lifshitz-Gilbert equation. The behavior of bit patterned media is typically evaluated  using an atomistic approach. Optical spots are calculated using a finite difference time domain technique and heat flow is evaluated using the usual Fourier differential equation.