Space division multiplexing (SDM),high order modulation, digital coherent detection,and digital signal process have become the necessary technologies for realizing a optical fiber transmission system with ultra-large capacity, ultra-high rate, and ultra-long distance. SDM technology has become the key part to realize Pbit/s transmission, and has become a research hotspot in resent years. A multicore fiber amplifier with SDM is analyzed systematically. In this paper, the research progress of multicore amplifiers, including multicore erbium-doped fiber amplifiers, multicore few-mode erbium-doped fiber amplifiers, multicore erbium-ytterbium co-doped fiber amplifiers, multicore Raman amplifiers, multicore remote pump amplifier,and hybrid multicore amplifiers, are reviewed. Finally, the future of multicore amplifier technologies is prospected.