Glass is a material that has been used for a long time in windows as a filling material and has much to offer in this regard due to its possibility to carry high compressive stresses. For several years, there has been a trend in architecture to use glass not only as a part of the building envelope, but also as material for load-bearing elements. This represents a special challenge because of the glass brittleness. Knowing how to model the failure of such structures is then a very important challenge and can contribute to a decrease of the partial safety coefficients used in the design. Most of time, such a modeling needs to be based on a statistical approach. This is the case for glass beams in current zones. The present contribution focuses, in a first part, on the modeling of failure in annealed glass single panes using Weibull model extended to take into account the subcritical cracking. Then, in a second part, the modeling of laminated glass beams with a SGP interlayer is presented. This modeling is performed with the FE software Abaqus and takes into account the mechanical contribution of the interlayer thanks to a Mooney-Rivlin model. The special challenge is here to reproduce the post-peak behavior of the laminated glass beam and then the remaining load carrying capacity of the structure. The third part of the paper deals with the failure in connection area. Thanks to a combination of FE modeling, experimental campaigns and microscopy observations (with optical and electronic microscopes) the deterministic aspect of the failure in these special zones is put into evidence. This important result enables to simplify the modeling of the mechanical behavior of such area.