Despite tremendous progress seen in the computational fluid dynamics community for the past few decades, numerical tools are still too slow for the simulation of practical flow problems, consuming thousands or even millions of computational core-hours. To enable feasible multi-disciplinary analysis and design, the numerical techniques need to be accelerated by orders of magnitude. Reduced-order modeling has been considered one promising approach for such purposes. Recently, non-intrusive reduced-order modeling has drawn great interest in the scientific computing community due to its flexibility and efficiency and undergoes rapid development at present with different approaches emerging from various perspectives. In this paper, a brief review of non-intrusive reduced-order modeling in the context of fluid problems is performed involving three key aspects: i.e. dimension reduction of the solution space, surrogate models, and sampling strategies. Furthermore, non-intrusive reduced-order modelings regarding to some interesting topics such as unsteady flows, shock-dominating flows are also discussed. Finally, discussions on future development of non-intrusive reduced-order modeling for fluid problems are presented.