The Artificial Fish Swarm Algorithm (AFSA) is inspired by the ecological behaviors of fish schooling in nature, viz., the preying, swarming, following and random behaviors. Owing to a number of salient properties, which include flexibility, fast convergence, and insensitivity to the initial parameter settings, the family of AFSA has emerged as an effective Swarm Intelligence (SI) methodology that has been widely applied to solve real-world optimization problems. Since its introduction in 2002, many improved and hybrid AFSA models have been developed to tackle continuous, binary, and combinatorial optimization problems. This paper aims to present a concise review of the family of AFSA, encompassing the original ASFA and its improvements, continuous, binary, discrete, and hybrid models, as well as the associated applications. A comprehensive survey on the AFSA from its introduction to 2012 can be found in [1]. As such, we focus on a total of {\color{blue}123} articles published in high-quality journals since 2013. We also discuss possible AFSA enhancements and highlight future research directions for the family of AFSA-based models.