Volumetric additive manufacturing is a novel additive manufacturing method, offering advantages such as fast printing speed and isotropic mechanical properties. As the important branch of volumetric additive manufacturing, computed axial lithography based on the azimuthal projections and rotational printing has attracted great attentions and been widely used in recent years. Here, we focus on the projection algorithms of computed axial lithography, which is critical to the printing quality including its fidelity and accuracy. Different optimization methods including iterative optimization of projection space and objective model, optimization for the optical influences of materials and the optimizations cooperating with hardware upgrade are summarized. The features and advantages of different projection optimization algorithms are also analyzed and discussed, which may promote the applications and development of volumetric additive manufacturing.