In the past 40 years, the study and application of crop-response-to-fertilization function model has made significant progresses and has already become the main technical basis for and a branch system of the project of soil-test-based formulated fertilization. The quadratic polynomial model is the most commonly used fertilizer effect model under study and in application. This paper reviewed briefly progresses that have been made in the study on types, applicabilities, experimental designings and, parameter estimation empirical fertilizer effect models, class characteristic fertilizer effect models, non-typical recommended fertilization optimization method and combination of function methods with soil testing and so on. On such a basis, the paper points out that the prevailing fertilizer effect model in the present days has three problems, i.e. multicollinearity, heteroscedasticity and unreasonable professional hypothesis. In quadratic polynomial models strong multicollinearity exists between the one-degree term and the quadratic term, the one-degree term and its interaction effect terms, the quadratic term and its interaction effect terms, and in the square root polynomial model, exists severer multicollinearity. The serious multicollinearity causes errors in “+” or “-” signs of the model coefficient or difficulty to evaluate relationships between independent variables in contribution to crop yield. Model residual analysis shows that fitting residual error of the quadratic polynomial model displays a gradually dispersing funnel-like distribution pattern with increasing rice yield, which indicates that residual variance differs with yield level. Serious heteroscedasticity causes the least squares parameter estimation to be no longer valid, and t test and F test no longer reliable. Besides, the prevailing quadratic polynomial model has two defects in being conformable with practice, that was, linear relationship is used in the function between yield increment per kg nutrient and fertilization rate, and symmetrical relationship is in the function between yield-increasing effect of fertilization before the maximum rate and yield-reducing effect after the maximum rate, which makes it difficult to reflect the actual relationship quantitatively between field fertilization rate and crop yield in the field. The paper also analyzes causes of the problems and their diagnostic method. Therefore, it is suggested that in-depth study should be done to explore remedial measures to eliminate or relieve the impacts of the defects the multi-factor fertilizer effect model and proper conditions for its application, to develop non-structural fertilizer effect models so as to overcome the irrationality of the professional hypothesis of the empirical model, to unfold development of fertilizer effect parameter identification technologies on the basis of the large volumes of "3414" experimental data, and eventually to realize microscopic guidance using fertilizer effect models and to provide theoretical modeling basis for development of a software system for fertilization recommendation.