Low fidelity model assisted design optimization of turbomachines has reduced the total computational and experimental costs. These models are called surrogate models which mimic the actual experiments or simulations. The surrogate models can generate thousands of approximate results from a few samples, making it easy to locate the optimal solution. Ample articles reported surrogate assisted design optimization of centrifugal pumps. In this article, the authors try to give a brief overview of the surrogate based optimization technique along with its historical applications and trend of the recent use. The various key design parameters which affect the performance of the centrifugal pump have also been discussed. The effectiveness of the surrogate based optimization technique and corresponding performance metrics have been discussed.