Dating of building materials is one of the essential means for the History of Construction. Previous researches [1] on series of western European monuments showed that in the Middle-Ages the practice of re-using bricks originating from older structures was a frequent phenomenon. Therefore, dating of bricks by luminescence or archaeomagnetism is not always representative for the erection of the masonry, the moment to be dated. That is why we have focused on mortar dating for the last 6 years. Numerous attempts in mortar dating concentrated on the radiocarbon method which has, however, its limitations [2], but also its potential and hopes [3]. Thanks to our 6-year experience, OSL has become today fully usable for dating monuments of known ages. The basic premise in such analysis is that quartz in the sand used for making mortar is optically zeroed during the preparation process (optical bleaching). The moment to be dated is the last exposition of mortar to light, before being embedded within the masonry and hidden from light. But, one of the problems encountered is the possible partial and heterogeneous bleaching of grains that led us to use a priori the single grain technique (SG-OSL). We will present some aspects of the methodology for dating mortars by SG-OSL, in comparison with standard multi-grain OSL. A summary of the latest development of the theoretical approach that led us to imagine a new way of statistical treatment (the so-called EED model, as exponential exposure distribution [4]) will be presented and discussed. Finally, a good agreement between OSL and reference ages for a series of samples from a variety of ages and situations was obtained even in case of poorly bleached material [5]. We will also present cases for which we still encounter some difficulties in dating them by SG-OSL (low sensitivity mortar samples, samples resulting from a mixture of sediment and calcareous stones …). Such cases imply that characterization of dated mortars represents an essential step of the dating procedure. Anyway, the actual situation of the OSL dating methodology justifies today the systematic use of SG-OSL in determining chronologies of masonries imprecisely dated, as frequently encountered for the late Roman Antiquity and the Early Medieval periods in Western Europe. [1] P. Guibert, I. Bailiff, M. Baylé, S. Blain, A. Bouvier, S. Büttner, A. Chauvin, Ph. Dufresne, A. Gueli, Ph. Lanos, M. Martini, D. Prigent, C. Sapin, E. Sibilia, G. Stella, O. Troja, The use of dating methods for the study of building materials and constructions: state of the art and current challenges, Proceedings of the 4th International Congress on Construction History, Paris 3-7 July 2012, 469-480, 2012. [2] G. Pesce, R. J. Ball, Dating of Old Lime Based Mixtures with the Pure Lime Lumps Technique, In: Nawrocka D. M. (ed.) Radiometric Dating, InTech, 21-39, 2012. [3] J. Heinemeier, Å. Ringbom, A. Lindroos, ÁE Sveinbjörnsdóttir. Successful AMS 14C dating of nonhydraulic lime mortars from the medieval churches of the Åland Islands, Finland. Radiocarbon, 52(1),171–204, 2010. [4] P. Guibert, C. Christophe, P. Urbanová, S. Blain, G. Guérin. Modeling incomplete and heterogeneous bleaching of mobile grains partially exposed to the light: towards a new tool for single grain OSL dating of poorly bleached mortars, Radiation Measurements, 107, 48-57, 2017. [5] P. Urbanová, P. Guibert. A methodological study on single grain OSL dating of mortars: comparison of five reference archaeological sites. Geochronometria, 44, 77-97, 2017.