A detailed understanding of the gain and phase characteristics of discrete-time zeros and poles is obtained. This new knowledge extends and complements previous results available in the control systems and digital signal processing literature. The results introduced in the paper also substantiate the view that discrete-time zeros and poles have much more intricate frequency domain features than their continuous-time counterparts. A simple loop-shaping example is used to illustrate the feasibility of discrete-time control System design developed entirely in the z-plane.