Piecewise-flat surfaces encode 3D shapes across science and engineering. Intrinsic triangulations offer an alternate perspective, representing a discrete surface not by a location of each vertex, but instead by a length of each edge. This change in perspective creates a bridge between rich theory in geometry and topology, and powerful new algorithms in geometric computing. In this talk, we will introduce some basic concepts in the discrete geometry of surfaces, and view them through the lens of intrinsic triangulations. No prior knowledge of the subject is required.