Gamma-ray bursts (GRBs) associated with gravitational wave events are, and will likely continue to be, viewed at a larger inclination than GRBs without gravitational wave detections. As demonstrated by the afterglow of GW170817, this requires an extension of the common GRB afterglow models which typically assume emission from an on-axis top hat jet. We present a characterization of the afterglows arising from structured jets, providing a framework covering both successful and choked jets. We compute new closure relations for structured jets and compare with the established relations for energy injection and refreshed shock models. The temporal slope before the jet break is found to be a simple function of the ratio between the viewing angle and effective opening angle of the jet. A numerical model to calculate synthetic light curves and spectra is publicly available as the open source Python package afterglowpy.