•State of the art on the confinement of masonry and concrete with FRM.•State of the art on analytical prediction of the compressive strength of FRM-column.•Two new DOMs for the FRM-confined column.•Two simplified versions of the proposed DOMs. As well known the confinement is an effective intervention for increasing the compressive strength of an axially loaded column. During the decades, different materials have been adopted in order to provide confining action, such as steel, reinforced concrete and latest high-performance fibers. Fibers application resulted a powerful solution mainly because of the high ratio between mechanical properties and weight and the absence of electrochemical corrosion. On the other hand, fiber needs to be impregnated with a matrix in order to be applied around the column and to exert an effective confining pressure. Polymers manifest excellent performance in this role, but unfavorable result if breathability of the structural element is a key-issue as well as reversibility and compatibility of the new materials with the existing substrates (e.g. in historical masonry construction). In this scenario, the interest in non-polymeric matrix has been increased in the last years, as the use of a cement/lime based mortar. In the present paper, a state-of-art regarding experimental programs on concrete and masonry samples confined by Fiber Reinforced Mortar (FRM) and subjected to pure compressive test is preliminary reported. Therefore, a multiple linear regression analysis was implemented in order to identify the possible influence of the interaction between the properties of the matrix and those of the fibers on the effectiveness of the confining pressure. Two new analytical formulations were assessed and discussed in the present study (the first related to concrete and the second related to masonry columns), evidencing the importance of taking into account the characteristics of the confining mortar besides those of fibers. A deep comparison (experimental vs. predicted) of the proposed formulae with Design-Oriented-Models (DOM) from the literature was also provided in terms of accuracy, precision and correlation. Finally, simplified relationships are also furnished and addressed to a possible contribution for design guidelines on the topic.