Line waves (LWs) are newly discovered wave phenomena that can be seen as the lower-dimensional analogs of surface waves. They are localized in two dimensions (both in-plane and out-of-plane), channeling energy flow along a 1-D track, and can be supported by suitable planar discontinuities in the surface impedance of both artificial (metasurfaces) and natural (e.g., graphene) low-dimensional materials. Recent studies have explored various aspects of LW electromagnetics, including analytical and numerical modeling, potential material platforms, physical properties, and coupling effects. In this chapter, we provide a concise overview of these key findings, highlighting open challenges and potential research directions.