Plasma-based accelerators represent one of the most exciting concepts in high-gradient particle acceleration. The two major approaches to plasma-based acceleration are defined by the way plasma waves are excited: either by relativistic electron bunches for a plasma wakefield accelerator (PWFA) or by ultra-intense laser pulses for a laser wakefield accelerator (LWFA). In the highly nonlinear regime of such wakefield generation, the intense laser radiation pressure or beam fields expel all of the plasma electrons, forming a region completely devoid of electrons (plasma “bubble”) that propagates behind the driver. Two major accelerating mechanisms can be found in a plasma bubble: electrons either gain energy from the "static" longitudinal wakefield (near-field type) or when condition permits, gain energy from a transverse electromagnetic wave (far-field type) that resonantly interacts with electrons being focused and undergoing betatron motion. The study of state-of-art plasma-based accelerators is rooted in the research of the acceleration platform (plasma structure) and the accelerating mechanisms (both near-field and far-field types). This work will present a study of the formation of the acceleration platform and the interplay between different accelerating mechanisms, through analytic modeling and numerical simulations. Advanced concepts for particle accelerations in plasmas are also proposed with the design of new platforms, or by taking advantage of the combinations of different accelerating mechanisms. First, the theory of quasistatic approximation is advanced and the excitation of nonlinear plasma bubble by a point-like ultra-relativistic charge is investigated. The phenomenological model of plasma bubble is developed for various beam charges, and the mechanism of the bubble formation is explained by developing simple models of the bubbles at large charges. Then, inside the idealized plasma bubble/channel, the interplay of tightly focused laser fields (far-field) and wakefields (near-field) is studied. It is shown that the longitudinal and transverse components of laser electric fields always counteract each other, and essentially decrease the final energy gain of electrons via the direct laser acceleration (DLA) mechanism. The electron energy gain from the wakefield is substantially compensated by the energy loss to the longitudinal laser field component. Next, it is demonstrated that the direct laser acceleration of the driver electron beam by a co-propagating laser beam is beneficial for extending the lifetime of the plasma acceleration structure. Using numerical simulations, it's shown that the two beams interact synergistically and extend each other's travel distances. The key interactions responsible for the synergy are found to be laser channeling by the electron bunch, and direct laser acceleration of the bunch electrons by the laser pulse. Implications of such synergistic interactions for the high-gradient acceleration of externally injected witness charges are discussed, and a new concept of a Laser-pulse and Electron-bunch Plasma Accelerator (LEPA) is formulated. At last, gears are switched to over-dense plasma, a novel concept of laser-ion lensing and acceleration (LILA) is introduced. Using a simple analogy with an optical lens, the simultaneous focusing and acceleration of ions are accomplished by illuminating a shaped solid-density target with an intense laser pulse at $\sim 10^{22}$W/cm$^2$ intensity and using the radiation pressure of the laser to deform/focus the target into a cubic micron spot. The LILA process is approximated using a simple deformable mirror model, and then validate it using three-dimensional particle-in-cell simulations. Through extensive scans of the laser and target parameters, stable focusing is found at different laser powers (from few- to multi-petawatt) and different target configurations (hydrogen target to polymer target). Focused ion beams with the focused density of order $10^{23}$cm$^{-3}$ and energy density up to $2\times10^{13}$J/cm$^3$ at the focal point are predicted for future multi-petawatt laser systems.