In this work, a wide experimental dataset about the axial behavior of masonry columns confined with Fabric Reinforced Cementitious Matrix (FRCM) jackets (also refered to as TRM - Textile Reinforced Mortar or TRCC - Textile Reinforced Cementitious Composites), that contains the results from 226 confined specimens, was collected. Data were critically analyzed with the aim of identifying the influence of the most important parameters considered within the dataset (i.e., fibers type and number of layers, masonry type and unconfined strength, mortar type and mechanical strength, the effective lateral pressure, etc.). Further, a review of the main models proposed in different Codes and in literature was carried out, which were then applied to the dataset, highlighting some discrepancies in their predictions. Thus, a new formulation for the confined strength of masonry columns was proposed, aiming to consider also some other influencing variables such as the compressive strength of the masonry blocks and that of the mortar joint. Lastly, the validity of the proposal was verified on a new set of experimental results, which were obtained by the authors testing three unconfined and confined clay brick masonry columns. Specimens were subject to monotonic axial loading under displacement control until failure, and stress and strains were monitored continuously during the test. The jacketing system was realized with one layer of glass-based FRCM (GFRCM).