Particle acceleration in astrophysical plasmas has been a longstanding and challenging problem and it has been both intensively and extensively highlighted by the recent observations from Compton Gamma Ray Observatory on various astrophysical objects, including Gamma Ray Bursts (GRBs), Active Galactic Nuclei (AGNs) and Galactic Black Hole Candidates (gBHCs). In this work, I study the stochastic particle acceleration due to the resonant interactions between the turbulent plasma waves and particles. I employ the particle orbital theory approach by treating the effects of various waves as perturbations to particle's zeroth-order Hamiltonian. The particle's momentum and pitch angle diffusion coefficients (D\sbpp, D\sbμμ) are derived for interactions of proton/Alfven-wave, electron/fast-magnetosonic-wave and electron /whistler-wave, though the formalism can be generalized to other type of waves. Based on the Monte Carlo code I have developed, which solves the coupled time-dependent wave, particle, and photon kinetic equations, these results have been or are being applied to the central region of both AGNs and gBHCs, with applications for gamma-ray production and energetic particle outflows. By calculating the particle trajectories under the influence of gravity and radiation pressure near the center of galactic black hole accretion disk, I show that the recent discoveries of relativistic outflows from several X-ray binaries (e.g., GRS1915+105 and GROJ1655$-$40) can be well explained by radiation acceleration. The calculated final jet velocity is in good agreement with the observations and further constraints can be put on the composition and the power of those jets. The isotropic but inhomogeneous distribution of GRBs over the whole sky apparently requires more exotic explanations. A novel model for GRBs from high velocity neutron stars, which escape into our Galactic halo, has been developed. I show, in detail, the difficulties the halo models are facing and propose several scenarios to overcome them. This model predicts that bright burst distribution should deviate from isotropy and it still awaits confrontation with the observations.