We will present two basic results from the global differential geometry of curves in 3-dimensional space: Fenchel's Theorem, that the total curvature of a closed curve is greater than or equal to 2*pi, with equality if and only if the curve is plane and convex, and the Fary-Milnor Theorem, that the total curvature of a knotted curve is greater than 4*pi. We will present two approaches to these theorems: one based mostly on the theory of curves, one based mostly on the theory of surfaces.