This paper presents a new method for classification and characterization of voltage dips and swells in electricity networks. The proposed method exploits unique signatures and parameters of three phase voltage signals extracted from the polarization ellipse in three-dimensional (3D) co-ordinates. Five ellipse parameters, which include azimuthal angle, elevation, tilt, semi-minor axis and semi-major axis, are used to classify and characterize voltage dips and swells. Seven types of voltage dips, which include a total of 19 groups of dips incorporating different kinds of balanced (three-phase dips) and unbalanced (single-phase or double-phase) dips, are identified and successfully classified using the 3D polarization ellipse parameters. Two types of voltage swells, which include a total of 6 groups, are also classified using the proposed method. The proposed method is validated using real measurement data, recorded waveforms provided by the IEEE 1159.2 working group, and the data of unbalanced dips associated with phase angle jumps, voltage drops and rotations due to loading effects.