In this paper, we review our latest progress for heat-assisted magnetic recording (HAMR) systems. The temperature distribution has been computed using the finite difference time domain technique and by solving the heat diffusion equation. Magnetic behavior has been calculated using a renormalized cell technique (granular media) and atomistic simulation [bit-patterned media (BPM)]. We find that the ultimate density of HAMR on granular media depends greatly on grain size, with a 5 nm grain pitch yielding $\sim 4$ Tb/in2. We were unable to exceed $\sim 5.8$ Tb/in2 on BPM owing to excessive heating of the adjacent track, causing adjacent track erasure to date. Shingled recording on granular media, using two dimensional magnetic recording (TDMR) detection depends greatly on the mechanical systems, with likely user densities reaching $\sim 2.5$ Tb/in2. Finally, shingled recording without heat assist on BPM yielded an unexpectedly high density of $\sim 8$ Tb/in2.