L1(0)-ordered FePt and CoPt (collectively called L1(0)-Fe(Co)Pt in this review) have become potential materials for future ultrahigh density perpendicular magnetic recording (PMR) media due to their high magnetocrystalline anisotropy, rendering small grains with high thermal stability. However, PMR media using such high anisotropy faces the well-known trilemma issues among thermal stability, signal-to-noise ratio (SNR), and writability. This paper will provide an overview of the impact of L1(0)-Fe(Co)Pt on overcoming the superparamagnetic limit and balancing the trilemma issues for ultrahigh density PMR media. Here the research and development of L1(0)-Fe(Co)Pt materials will be presented, from the perspectives of enhancing thermal stability, SNR and writability. Furthermore, we will provide some combined approaches to tackle the challenges in balancing the trilemma issues, focusing on materials engineering.