The terahertz frequency band is located between infrared and microwave in the electromagnetic spectrum. The interesting properties such as broadband, low energy, high permeability, fingerprint, etc. make terahertz wave important for applications in the fields of aerospace, wireless communications, security, materials science, biomedicine, etc. The development and application of terahertz science and technology are largely limited by the terahertz sources, therefore it is crucial to develop new terahertz radiation sources. Recently, it was shown that terahertz spintronic not only provides the possibility of physically controlling the femtosecond spin current, but also expects to be the next-generation ultra-wideband, low-cost, high-efficiency terahertz sources. In this paper we systematically review the historical development, experimental devices, emission mechanisms, material selections, and future prospects of the spintronic terahertz sources. We present the research advances in the physical mechanisms of ultrafast spin current induced by femtosecond laser, the spin charge conversion at ferromagnetic and non-magnetic interfaces, and the terahertz emission triggered by ultrafast pulses. This review also introduces spintronic terahertz sources based on heavy metals, topological insulators, Rashba interfaces, and semiconductor systems.