Flexible job shop scheduling problem (FJSP) is one of important issues in the integration of research area and real-world applications. The traditional FJSP always assumes that the processing time of each operation is fixed value and given in advance. However, the stochastic factors in the real-world applications cannot be ignored, especially for the processing times. In this paper, we consider FJSP model with uncertain processing time represented by fuzzy numbers, which is named fuzzy flexible job shop scheduling problem (F-FJSP). We firstly review variant FJSP models such as multi-objective FJSP (MoFJSP), FJSP with a sequence dependent & set time (FJSP-SDST), distributed FJSP (D-FJSP) and a fuzzy FJSP (F-FJSP) models. We secondly survey a recent advance in hybrid genetic algorithm with particle swarm optimization and Cauchy distribution (HGA+PSO) for F-FJSP and hybrid cooperative co-evolution algorithm with PSO & Cauchy distribution (hCEA) for large-scale F-FJSP. We lastly demonstrate the HGA+PSO and hCEA show that the performances better than the existing methods from the literature, respectively.