This thesis is dedicated to the design of novel wideband dual-frequency patch antenna elements and arrays for base stations of wireless communication systems. An innovative dual-frequency technique for patch antenna, which provides numerous advantages over traditional designs, is proposed. Several extensions and arrays based on the proposed dual-frequency technique are designed and studied for particular applications and high performance. Moreover, the application of this dual-frequency technique for cylindrical patch antennas is implemented. This research aims to provide advanced patch antenna designs for today or future wideband multi-frequency systems with various diversity and frequency reuse techniques. At the beginning, a shorted patch antenna proximity-coupled by a combined Land T-probe feed structure is proposed, which achieves two very wide impedance bandwidths, around 50% for each, with a tunable frequency separation. In spite of its wide bandwidth, this antenna exhibits spurious radiation. And like most conventional dual-frequency antennas, it is not suitable for the construction of antenna array. Therefore, by embedding shorting vias, a novel L-probe fed patch antenna for wideband and dual-frequency operation is proposed. This antenna consists of two patches in a stacked configuration for producing two operating bands independently. The proper use of shorting vias realizes good impedance matching for both frequency bands and limits unwanted radiations. This antenna successfully achieves all the criteria for an ideal dual-frequency patch antenna, including two wide impedance bandwidths, similar and sound radiation patterns, tunable frequency ratio in a large range and the unique potential for array application. Therefore, it is selected as the basic structure in following researches. To further explore its wideband capability, a stacked patch is introduced to this dual-frequency antenna so as to achieve two wide impedance bandwidths (S11<-14dB) of 22.2% and 39% for the lower and upper band, respectively. Next, some extensions of the proposed dual-frequency patch antenna are designed and fabricated to satisfy particular applications. For compact size, a wideband dual-frequency patch antenna with a common shorting wall is proposed, which obtains wide impedance bandwidth of 54.0% and 50.4% for the lower and upper frequency bands, respectively, with a projection area reduced by 71.5% compared to a regular square half-wavelength patch antenna. On the other hand, a single feed dual-frequency patch antenna with simplified structure is designed for lower cost and ease of fabrication. Proper compact filters are studied and introduced to this antenna to block the unwanted current flow in certain frequencies. In spite of its simple structure, this antenna retains two wide impedance bandwidths (21% and 25.3% referred to -14dB return loss) and all the other advantages of the basic design. To verify the unique array capability of the proposed dual-frequency technique, two dual-frequency patch antenna arrays based on this technique for linear- and dual-polarization operations are designed and fabricated. Firstly, a 9-element dual-frequency patch array with linear-polarization is proposed. In virtue of the reconfigurable structure of the proposed dual-frequency element, the radiating elements for different frequencies are arranged alternately in a stacked manner to form the array. As a result, the severe problem related to the element spacing, which precludes the applications of most conventional dual-frequency patch antennas in array, is greatly alleviated or even eliminated, and therefore good radiation patterns are achieved in both bands. The research shows that this array exhibits a wide -10dB impedance bandwidth of 24.5% and 40.0% for the lower and upper band, correspondingly, as well as similar and excellent radiation patterns in both bands with low cross-polarization and large front-to-back ratio. A guideline of proper arrangement of the radiating elements with different frequency ratio for good patterns is demonstrated. To further provide polarization diversity for system capacity enhancement, a wideband dual-frequency dual-polarization patch antenna array is proposed based on the proposed dual-frequency antennas structure. Two techniques are used to conquer the coupling between polarizations of this array. One is phase cancellation feeding networks and the other is auxiliary metallic isolation-walls. This array provides two wide -14dB impedance bandwidths covering 0.82-0.96GHz and 1.71-2.17GHz for both polarizations, and a high isolation exceeding 30dB over the whole passbands. Patch antenna arrays mounted on a cylindrical ground are suitable for angle diversity and frequency reuse systems for further increase of the system capacity. In this thesis, the wideband L-probe fed patch antennas and arrays with a cylindrical ground are studied by both numerical and analytical methods. The curvature effects on the impedance matching and radiation patterns are investigated in detail, and the radiation patterns of vertical and circular array are studied. It is discovered that the impedance bandwidth of planar patch antenna can be greatly increased by the curved grounding structure. The relevant operating principle is demonstrated afterward. Finally, the proposed dual-frequency technique is further introduced to a cylindrical patch antenna, and its characteristics are studied in comparison with the one on a flat ground. In virtue of the curvature effect, this dual-frequency cylindrical patch antenna achieves a wider impedance bandwidth of 29.3% in the lower band and a similar impedance bandwidth of 38.8% in the upper band. All the proposed dual-frequency patch antennas and arrays exhibit two very wide impedance bandwidths with tunable frequency ratio, so they are suitable to serve as base station antennas for almost all the cellular communication systems today.