The novel designs of circular microstrip antennas have been investigated in this dissertation. In the linearly polarized designs, the study of single-feed dual-frequency circular microstrip antenna with an open-ring slot has been firstly presented. As for the broadband circular microstrip antenna designs, antennas with two open-ring slots, embedded reactive loading by probe feed and microstrip-line feed have been presented. The antenna bandwidth of them can be enhanced about 4% to 6%. In the circularly polarized designs, we have proposed a circularly polarized microstrip antenna with a spur line. By choosing a suitable length of the spur line, CP operation can be obtained. And then, such a design can be applied to a compact circular patch antenna with bent slots. These reduced the antenna size to be 40%~50% of that of the simple case. Finally, we use the ideas of CP operation with elliptic patch and dual-frequency operation with stacked patch to propose a dual-band circularly polarized stacked elliptic microstrip antenna design. The frequency ratio of this design is about 1.39.