The interaction between ultrashort intense laser pulses and solid-target plasmas can generate ultra-broadband, high-field terahertz (THz) radiation with their pulse energy ranging from tens of microjoule to over 100 mJ, spectral bandwidth covering far beyond the entire THz band, peak electric field strength reaching to tens of MV/cm, and peak magnetic field strength getting to several Tesla. The characteristics and parameters of these THz radiation depend on different laser parameters and targeting conditions, which can be attributed to different generation mechanisms. In this paper, several main mechanisms or theoretical models and their typical experiments involved on the interaction of ultrafast intense lasers pulses with solid-target plasmas for generation of high-field THz radiation are reviewed. Understanding of these mechanisms will be helpful for active modulation and optimization of these THz sources to improve the energy conversion efficiency. Due to their strong peak electric and magnetic fields, these pulsed THz sources will show many important, novel potential applications in many fields such as physics, chemistry, materials, and biomedical science.