Heat-assisted magnetic recording is one of the most promising approaches to achieve extremely high density magnetic recording. A laser is used to temporarily heat the recording media film to render its switching field to become lower than the magnetic field of the writing head. After writing, the film material is cooled down to room temperature for data storage. In this dynamic writing process, the challenge is to tailor and optimize the time resolved structural/thermal/magnetic properties of the media films and their correlations during/after the laser heating. In this paper, the four dimensions of current progress in HAMR media research, i.e., structure, magnetic properties, thermal properties and time, are briefly overviewed and discussed. Their correlations are also emphasized.