In this paper, we give a brief introduction of the parallel error diffusion and classify various approaches into three classes - partitioned area, concurrent, and inter-area error diffusions. These approaches, including intra-dot diffusion, space-filling curve traversal, Fibonacci-like sequence, multi-center dot diffusion, dispersed-dot diffusion, concurrent processing, neural network, and inter-dot diffusion are discussed and examples are given. Comparisons are made with other deterministic error filters (e.g. Floyd-Steinberg, Schroeder, Stucki, and Shiau-Fan) and with the corresponding clustered-dot and dispersed-dot ordered dithers. We also provide several extensions to the existing techniques. The conditions for parallel line error diffusions of horizontal, vertical, and diagonal lines are recognized and new parallel error diffusions are developed.