Crops need adequate mineral nutrition to ensure optimal growth and yield. Nitrogen (N) and phosphorus (P) are two major elements that are essential for crop growth. However, situations of N-P colimitation are frequent in agroecosystems. Hence, our ability to optimize crop production under these conditions depends on our ability to analyze and predict the response of crops to colimitation. Traditionally, agronomists rely on the law of the minimum (LM) to manage colimitation situations. This law states that crop growth is constrained by the most limiting element. In contrast, the multiple limitation hypothesis (MLH) argues that crops can adapt by balancing their resource allocation with the best compromise to maximize their growth. These two hypotheses result in contrasting growth response patterns. The aim of the present review is to identify the crop response pattern to N-P colimitation through an assessment of experimental results against a conceptual framework and to report the main mechanism involved in this interaction. Finally, an inventory of existing crop models handling N-P colimitation is presented and possible ways of improvement are proposed. This review allowed us to (1) remind of the published theories used to classify colimitation types, (2) highlight the fact that a large range of crops mostly showed MLH-response patterns, (3) report that the variability in crop response patterns is linked to pedoclimatic variation, (4) identify multiple mechanisms that may be involved in plant adaptation to N-P colimitation, (5) suggest that the interplay between the different mechanisms results in complex responses that are difficult to understand experimentally, (6) report that few models handle N-P colimitation and that most of them rely on the law of the minimum, and (7) recommend possible ways to improve model formalization for a better simulation of crop responses under N-P colimitation.