The origin of high-energy particles in the universe is one of the key issues of high-energy solar physics, space science, astrophysics, and particle astrophysics. During cosmic explosions, some charged particles in the background plasma can be accelerated to very high energies by electric fields. Based on the characteristics of interactions between charged particles and electric fields carried by the background plasma, the mechanisms of charged particle acceleration can be divided into several groups: resonant interactions between plasma waves and particles, acceleration by electric fields parallel to magnetic fields, and acceleration caused by drift of the guiding center of particle gyro-motion around magnetic fields in magnetic field in-homogeneity-related curvature and gradient, etc. According to macroscopic energy conversion mechanisms leading to acceleration of particles, several theories of particle acceleration have been developed: stochastic particle acceleration by turbulent electromagnetic fields, diffusive shock acceleration of particles, and particle acceleration during magnetic re-connections. These theories have their own assumptions and characteristics and find applications in different astrophysical contexts. With advances in high-energy astrophysical observations and in combination with analyses of characteristics of high-energy particle acceleration and radiation, we can better understand the underlying physical processes in dramatically evolving astrophysical environments.