The artificial magnetic conductor (AMC) and electromagnetic band gap (EBG) characteristics of planar periodic metallic arrays printed on grounded dielectric substrate are investigated. The currents induced on the arrays are presented for the first time and their study reveals two distinct resonance phenomena associated with these surfaces. A new technique is presented to tailor the spectral position of the AMC operation and the EBG. Square patch arrays with fixed element size and variable periodicities are employed as working examples to demonstrate the dependence of the spectral AMC and EBG characteristics on array parameters. It is revealed that as the array periodicity is increased, the AMC frequency is increased, while the EBG frequency is reduced. This is shown to occur due to the different nature of the resonance phenomena and the associated underlying physical mechanisms that produce the two effects. The effect of substrate thickness is also investigated. Full wave method of moments (MoM) has been employed for the derivation of the reflection characteristics, the currents and the dispersion relations. A uniplanar array with simultaneous AMC and EBG operation is demonstrated theoretically and experimentally.