Permanent-magnet linear motors (PMLMs) are widely used in various fields of industrial production, and the optimization design of the PMLM is increasingly attracting attention in order to improve the comprehensive performance of the motor. The primary problem of PMLM optimization design is the establishment of a motor model, and this paper summarizes the modeling of the PMLM electromagnetic field. First, PMLM parametric modeling methods (model-driven methods) such as the equivalent circuit method, analytical method, and finite element method, are introduced, and then non-parametric modeling methods (data-driven methods) such as the surrogate model and machine learning are introduced. Non-parametric modeling methods have the characteristics of higher accuracy and faster computation, and are the mainstream approach to motor modeling at present. However, surrogate models and traditional machine learning models such as support vector machine (SVM) and extreme learning machine (ELM) approaches have shortcomings in dealing with the high-dimensional data of motors, and some machine learning methods such as random forest (RF) require a large number of samples to obtain better modeling accuracy. Considering the modeling problem in the case of the high-dimensional electromagnetic field of the motor under the condition of a limited number of samples, this paper introduces the generative adversarial network (GAN) model and the application of the GAN in the electromagnetic field modeling of PMLM, and compares it with the mainstream machine learning models. Finally, the development of motor modeling that combines model-driven and data-driven methods is proposed.