Turbulent magnetic fields are ubiquitous in space physics and astrophysics. The influence of magnetic turbulence on the motions of charged particles contains the essential physics of the transport and acceleration of energetic charged particles in the heliosphere, which is to be explored in this thesis. After a brief introduction on the energetic charged particles and magnetic fields in the heliosphere, the rest of this dissertation focuses on three specific topics: 1. the transport of energetic charged particles in the inner heliosphere, 2. the acceleration of ions at collisionless shocks, and 3. the acceleration of electrons at collisionless shocks. We utilize various numerical techniques to study these topics. In Chapter 2 we study the propagation of charged particles in turbulent magnetic fields similar to the propagation of solar energetic particles in the inner heliosphere. The trajectories of energetic charged particles in the turbulent magnetic field are numerically integrated. The turbulence model includes a Kolmogorov-like magnetic field power spectrum containing a broad range of scales from those that lead to large-scale field-line random walk to small scales leading to resonant pitch-angle scattering of energetic particles. We show that small-scale variations in particle intensities (the so-called "dropouts") and velocity dispersions observed by spacecraft can be reproduced using this method. Our study gives a new constraint on the error of "onset analysis", which is a technique commonly used to infer information about the initial release of energetic particles. We also find that the dropouts are rarely produced in the simulations using the so-called "two-component" magnetic turbulence model (Matthaeus et al., 1990). The result questions the validity of this model in studying particle transport. In the first part of Chapter 3 we study the acceleration of ions in the existence of turbulent magnetic fields. We use 3-D self-consistent hybrid simulations (kinetic ions and fluid electrons) to investigate the acceleration of low-energy particles (often termed as "injection problem") at parallel shocks. We find that the accelerated particles always gain the first amount of energy by reflection and acceleration at the shock layer. The protons can move off their original field lines in the 3-D electric and magnetic fields. The results are consistent with the acceleration mechanism found in previous 1-D and 2-D simulations. In the second part of Chapter 3, we use a stochastic integration method to study diffusive shock acceleration in the existence of large-scale magnetic variations. We show that the 1-D steady state solution of diffusive shock acceleration can be significantly modified in this situation. The results suggest that the observations of anomalous cosmic rays by Voyager spacecraft can be explained by a 2-D shock that includes the large-scale magnetic field variations. In Chapter 4 we study electron acceleration at a shock passing into a turbulent magnetic field by using a combination of hybrid simulations and test-particle electron simulations. We find that the acceleration of electrons is greatly enhanced by including the effect of large-scale magnetic turbulence. Since the electrons mainly follow along the magnetic lines of force, the large-scale braiding of field lines in space allows the fast-moving electrons interacting with the shock front multiple times. Ripples in the shock front occurring at various scales also contribute to the acceleration by mirroring the electrons. Our calculation shows that this process favors electron acceleration at perpendicular shocks. We discuss the application of this process in interplanetary shocks and flare termination shocks. We also discuss the implication of this study to solar energetic particles (SEPs) by comparing the acceleration of electrons with that of protons. The intensity correlation of electrons and ions in SEP events indicates that perpendicular or quasi-perpendicular shocks play an important role in accelerating charged particles. In Chapter 5 we summarize the results of this thesis and discuss possible future work.