The interaction of ultra-intense and ultrafast laser pulses with matter has paved the way for generation of ultrashort pulses in the attosecond timescale and coherent radiation in the extreme ultraviolet (XUV) and soft X-ray region at a table-top size. On one hand, it provides attosecond temporal resolution and atomic spatial resolution for ultrafast electron dynamics in atoms, molecules and condensed matters; on the other hand, it inspires the great potential of optical frequency comb (OFC) in precise measurements of transition frequencies and hyperfine splitting, a verification of basic physical constants such as the Rydberg constant, and the research on precise optical atomic clocks. With the expansion of the above-mentioned scientific researches, the repetition rate of the driving source has become the key factor to break through the measurement accuracy obstacles. Therefore, the research on high-repetition rate ultrafast laser technology for driving high-order harmonic generation (HHG) commences. In this paper, the high repetition rate HHG as the starting point, the method applied, the main parameter indices and the technical difficulties of the driving source are summarized. This paper can be a reference for the future development of high-repetition rate ultrafast laser technology for driving HHG. First of all, the research involving femtosecond enhancement cavity (fsEC) using passive amplification is introduced. The repetition rate of the high-order harmonics as obtained from this method has exceeded 100 MHz, which serves as the main technical means to obtain OFC in the XUV region. However, key issues, such as dispersion control of the high-precision resonator and stabilization of femtosecond laser frequency, are still the focus for future research and the current application difficulties of fsEC technology. Secondly, the research on Ti:sapphire laser system, ytterbium (Yb) doped fiber laser system and Yb all-solid-state laser system are reviewed. The few-cycle femtosecond pulse output by the Ti:sapphire laser system has an extremely high peak power, and it is the main driving source for generation of high-order harmonics and isolated attosecond pulses. However, constrained by the average power of the Ti:sapphire laser system, it is difficult to increase the repetition rate of XUV laser pulses to hundreds kilohertz or even megahertz. The thin-disk laser oscillator and the Yb fiber amplifier can produce femtosecond pulses with high average power. By means of nonlinear spectral broadening and pulse compression, an extreme ultraviolet radiation with a repetition rate of 10 MHz has been obtained in the HHG process of gases, yet the system structure remains complex and the technical difficulty is still high. Meanwhile, the Yb all-solid-state femtosecond amplifier, which can directly produce ultrashort pulses with high peak power, serves as an ideal driving source to realize HHG with the repetition rate on the MHz level. In view of the development trends of high-repetition rate driving sources, and based on the research experience on high-power Yb femtosecond lasers of our group, we propose high repetition rate ultrashort all-solid-state Yb amplifier for driving MHz repetition rate HHG with sub -40 fs all-solid-state Yb oscillator as seed and key techniques of gain narrowing suppression, precise dispersion control and efficient thermal management. Finally, the parameters of various technical means in passive amplification and gain amplification, as well as the key problems that need to be solved, are summarized, and the development trends of high repetition rate ultrafast laser technology for driving HHG are prospected.