ABSTRACT ADDED - Many high-energy astrophysical sources — pulsars, PWN, magnetars, GRBs, and AGN (including blazar) jets — produce bright bursts of gamma-ray emission, often featuring rapid variability and nonthermal spectra. This calls for a powerful and efficient mechanism of particle acceleration to very high relativistic energies within a collisionless plasma environment. One of the most promising basic plasma processes for this is magnetic reconnection — a rapid rearrangement of magnetic field and violent release of magnetic energy. Reconnection is believed to power numerous explosive phenomena in space physics (e.g., solar flares and geomagnetic storms) and has also been invoked to explain gamma-ray flares in astrophysics. However, in contrast to conventional, solar-system examples, astrophysical reconnection processes can be affected by the radiation back-reaction on the accelerated particles. I will review the recent progress in understanding radiative magnetic reconnection — a new frontier in high-energy plasma astrophysics — including the development of our new radiative particle-in-cell code Zeltron, which self-consistently incorporates synchrotron and inverse-Compton radiation reaction, and its application to some fundamental problems in high-energy astrophysics. For illustration, I will consider the intense gamma-ray flares discovered by AGILE and FERMI in the Crab Nebula. The rapid (hours) variability and high (hundreds of MeV) photon energies in these flares challenge modern theories of astrophysical particle acceleration, in particular, by violating the standard synchrotron radiation reaction-imposed limit of about 100 MeV on the synchrotron photon energy, which holds in most traditional particle acceleration models. Using analytical arguments and Zeltron numerical simulations, I will show how relativistic magnetic reconnection can help circumvent this energy limit and thus explain the Crab flares. Finally, I will discuss some future prospects and open questions in radiative plasma astrophysics.