Multi-phase reactors exhibit chaotic behaviors due to the highly turbulent motions of bubbles and phase interactions, leading to the formation of a complex spatio-temporal flow structure. The instantaneous motions of bubbles and wakes were studied by local measurements of bubble and particle-velocity fluctuations, bubble-wake structure, bubble shape and orientation. The chaotic dynamics of bubble and particle motions in multi-phase reactors were characterized in terms of the correlation dimension obtained by the deterministic chaos analysis for the series of time intervals between successive bubbles or particles by means of the embedding method. Three different methods, the deterministic chaos analysis, the short-term predictability analysis and the rescaled range (R/S) analysis, were applied to the non-linear dynamics of multi-phase reactors. The scale-up effect in the dynamic behavior of multi-phase reactors was investigated by using columns of different diameters. In addition, the non-linear hydrodynamic motions of bubbles and particles in multi-phase reactors have been modeled by means of an ANN (Artificial Neural Network) trained with time series data of voidage fluctuations for gas and solid phases. By successively adapting its output to input, the ANN can generate time-series data for any superficial gas velocity. The bifurcation diagrams of both bubble and particle motions generated by the trained ANN demonstrated that the ANN is capable of predicting and modeling the chaotic dynamics of multi-phase reactors.