This video describes a new type of 3D curves, which generalizes the family of 2D Euler spirals. They are defined as the curves having both their curvature and their torsion evolve linearly along the curve. The utility of these spirals for curve completion applications is demonstrated. This video accompanies the paper presented in [4]. Categories and Subject Descriptors I.3 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations General Terms Algorithms, Design Keywords Euler spirals, 3D curves