Artificial hearts (blood pumps) exhibit excellent hydraulic performance and compatibility with blood. Improvement in blood pump performance depends on the design and optimization methods. This review summarizes relevant work on designing and optimizing centrifugal blood pumps. First, the progress of numerical simulation methods was reviewed. High-fidelity flow field numerical simulations are prerequisites for design and optimization. The parameter sensitivity studies are summarized mainly from the aspects of the impeller, volute, and clearances. Several commonly used design and optimization methods have been summarized, including parameter sensitivity research, orthogonal optimization, machine learning/genetic algorithms, and topology optimization. Finally, the prospects and challenges for designing and optimizing blood pumps are discussed. This review provides valuable references and guidance for the future design and optimization of blood pumps.