Magnetic reconnection is one of the most important processes in space plasmas, that explosively releases the stored magnetic energy into the plasma energy. Owning to its fundamental nature, it has attracted recent attention in high-energy astrophysical settings as well, where relativity plays a crucial role. However, relativistic properties of magnetic reconnection still remain elusive. In this talk, we introduce two frontier problems of relativistic magnetic reconnection in electron-positron pair plasmas. First, we discuss fluid/MHD properties of magnetic reconnection. We newly developed a relativistic two-fluid code to investigate the large-scale evolution of magnetic reconnection. It is found that relativistic reconnection also exhibits Petschek-type structure and that the reconnection becomes faster in highly relativistic regimes. The numerical procedures, analyses of the simulation results, and relevance for reconnection models will be presented. Second, we investigate kinetic processes in magnetic reconnection by means of particle-in-cell (PIC) simulations. In the late stage of reconnection, we discovered that the Weibel instability occurs near the reconnection jet front. The instability is driven by the anisotropy of the local plasma, and generates turbulent magnetic fields. The basic mechanism of the instability and its roles in the reconnection context will be discussed. Finally, implications for standard ion-electron reconnection will be briefly discussed.