The boundary of a space can be defined in a wide variety of ways. The talk will focus on three examples: the space of simple closed curves, the space of marked hyperbolic surfaces, and the space of flat metrics. For simple closed curves, one famous approach is the introduction of the curve complex. The Gromov boundary of the curve complex has plenty of interesting properties. The other common approach works for all three examples: the space of geodesic currents. We’ll take a look at the geometric interpretation of each boundary space and discuss the degeneration process toward the boundary.