Particle filtering is a very popular method for nonlinear/non-Gaussian state estimation, however, implementation of particle filters (PFs) with a high state dimension in real-time is a very challenging practical task because the computation is prohibitive. Parallel & distributed (P&D) computing is a natural way to deal with the computational challenges of PF methods in order to make them practical for large scale problems, such as multitarget multisensor tracking. This paper presents results on development, implementation and performance evaluation of computationally efficient parallel algorithms for particle and particle flow filters (PFFs) utilizing a Graphics Processing Unit (GPU) as a parallel computing environment. Proposed are state-of-the-art parallel PF and PFF implementations which are optimized for GPU architecture and capabilities. The proposed algorithms are applied and tested, via simulation, for tracking multiple targets using a pixelized sensor, and for a high-dimensional nonlinear density estimation problem. It is demonstrated by the obtained simulation results that the proposed parallel GPU implementations can greatly accelerate the computation of both PFs and PFFs, and thereby bring them closer to practical applications.