The realizing of the detection and control of ultrafast process conduces to understanding and remoulding the physical world at a microcosm level. The attosecond light source with attosecond temporal resolution and nanometer spatial resolution can realize real-time detection and manipulation of the atomic-scale electronic dynamics and relevant effects of the substances. Therefore, attosecond science is considered as one of the most important milestones in the history of laser science. and has been listed as an important scientific and technological development direction in the coming 10 years. High-order harmonic generation (HHG) from intense laser-matter interaction is one of the most important routes to breaking through the femtosecond limit and achieving brilliant attosecond pulse radiations, and thus having aroused great interest in recent years. After more than 20-year development, the research about attosecond pulse generation by laser-gas interaction has reached a mature stage. This method produces the shortest isolated pulse in the world to date, with a pulse width being only 43 as. However, this method based on ionization-acceleration-combination encounters inevitable difficulties in pursuing the relativistically intense attosecond pulses and the highest possible photon energy. Quite a lot of studies have proved that the HHG efficiency from laser-plasma interaction can be a few orders of magnitude higher than that in gaseous media, which makes it possible to produce pulses with shorter pulse width and higher photon energy. In this article, we introduce the main generation mechanisms, research progress and frontier applications of HHG through the laser-plasma interaction process. In Section 2, we introduce the HHG generation mechanisms, including coherent wake emission, which is used to describe the HHG process driven by a nonrelativistic laser; relativistic oscillating mirror, which can well explain most of HHG processes generated from plasma-vacuum interface in relativistic regime; coherent synchrotron emission, which is suited to explain the HHG synchronously emitted from isolated electron sheets. The research progress is summarized in Section 3 from the aspects of radiation efficiency, polarization characteristics, phase characteristics, generation and diagnosis of isolated attosecond pulses, etc. Frontier applications of these ultra-broadband intense attosecond pulses are presented in the last section, such as the study of electronic dynamics, process, coherent diffraction imaging, diagnosis of extreme states of matter, the generation of extremely intense fields, etc. Finally, an outlook on the future development trends and innovation breakthroughs is also presented.