Archimedean spiral resonators as the unit inclusion for a metamaterial structure is studied. These inclusions are very compact, which make them a good candidate for practical metamaterial applications. Equivalent circuit models and analytical design formulas are derived for monofilar and bifilar spiral resonators. The circuit parameters and resonance frequencies are directly predicted by the geometry of the spiral and dielectric substrate/resonator configuration. Numerical simulations on both bulk and planar designs show that the predicted resonance frequencies are accurate enough for a preliminary design. Finally, complementary spiral structures, that is, spiral-shaped apertures in the ground plane, are considered. Loading two transmission lines with a complementary monofilar and a complementary bifilar spiral resonator, two planar band rejection structures are built. Measured results for two prototypes present a good accuracy.