Single crystal fiber (SCF) is a combination of bulk crystal and conventional fiber, it has gradually become a research hotspot in the field of solid-state lasers because of the excellent physical and chemical properties accompanying with good thermal management. Laser heated pedestal growth (LHPG) and micro-pulling-down (μ-PD) growth methods are introduced in detail. Meanwhile, the research status about the fabrication of SCF and SCF lasers at home and abroad are summarized. Finally, combined with the current research foundation, the research prospects and development trends of SCF are analyzed.