The presence of glide symmetries in periodic structures can introduce beneficial modifications in their electromagnetic properties. The difference between glide and non-glide periodic structures is due to the distinctive coupling between their constituent sub-unit cells. In this paper, we describe the recent discoveries on the remarkable properties of glide-symmetric periodic structures, which include widened stopbands, reduced dispersion, as well as enhanced anisotropy and magnetic response. These properties are explained through canonical structures simulated with two methods: mode matching and multimode transfer-matrix analysis. We also review the recent use of these distinctive properties for solving technological problems in practical devices such as filters, gap waveguide components, low-leakage flanges, compressed lenses, low-reflected material transitions and leaky-wave antennas with applications in 5G terrestrial communication systems, millimetre-wave satellite systems and automated contactless measurement techniques.