Masonry compressive strength plays a crucial part in the response of historic and existing masonry buildings under both static and dynamic actions. Therefore, determining the compressive strength of masonry is essential for predicting the structural response of buildings to mechanical loading. Closed-form empirical expressions for predicting the compressive strength of masonry rely mostly on the compressive strength of the constituent materials and less often on geometric parameters. Such expressions are typically characterised by a narrow application spectrum and low accuracy. Artificial intelligence can be employed for clearly quantifying and mapping the influence of material and geometric parameters on the compressive strength of masonry. In this study an extensive and inclusive database of experimental results on the compressive strength of masonry was assembled. This database was used for training and validating a series of Back Propagation Neural Networks. Through rigorous statistical analysis of the predicted masonry compressive strength, the optimal machine learning architecture for the task was determined, leading to substantially more accurate predictions in comparison to all empirical expressions found in the literature. In turn, the architecture was employed for revealing and mapping the influence of the input parameters on the compressive strength of masonry, both individually and in combination, thus avoiding the “black box” nature of many studies in the area of complex artificial intelligence models.