Lifting is a main task for manual material handling (MMH), and it is also associated with lower back pain. There are many studies in the literature on predicting lifting strategies, optimizing lifting motions, and reducing lower back injury risks. This survey focuses on optimization-based biomechanical lifting models for MMH. The models can be classified as two-dimensional and three-dimensional models, as well as skeletal and musculoskeletal models. The optimization formulations for lifting simulations with various cost functions and constraints are reviewed. The corresponding equations of motion and sensitivity analysis are briefly summarized. Different optimization algorithms are utilized to solve the lifting optimization problem, such as sequential quadratic programming, genetic algorithm, and particle swarm optimization. Finally, the applications of the optimization-based lifting models to digital human modeling which refers to modeling and simulation of humans in a virtual environment, back injury prevention, and ergonomic safety design are summarized.