Antennas design procedure, especially in portable devices, has been influenced by the growing demand for development of modern wireless communications. Hence, antennas that are wideband, compact, low profile, low cost, and easy to integrate into printed circuits are required. The research described in this dissertation focuses on optimally design and analysis of compact, low profile, and planar wideband patch antennas for modern wireless communications, namely, an open slot wideband planar antenna, a dielectric loaded wideband antenna, a planar antenna with ultra-wideband performance, and an E-shaped patch antenna. A novel very compact planar antenna with wideband performance is proposed and investigated. The proposed antenna has a size of only 9.2 mm x 9.8 mm x 1.52 mm. The size miniaturization is achieved by inserting an open slot in the ground plane to reduce the phase velocity. The antenna has achieved an impedance bandwidth of 52.16% and a stable radiation patterns over a wider bandwidth with a size reduction about 88%. Optimization of a dielectric loaded antenna by using Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) technique to achieve wideband and ii symmetrical broadside radiation performance is presented. Simulation is used to investigate the frequency-domain performance, regarding return loss, gain, and radiation pattern. Experimental measurements have also been performed to validate the performance of the proposed antenna. The obtained results show that the proposed dielectric loaded antenna achieves a good impedance matching and radiation characteristics in the entire band of WLAN IEEE 802.11a. A new ultra-wideband low profile microstrip antenna is presented for wireless applications. The proposed antenna has a compact size of 20x16 mm2 and an impedance bandwidth of 134.88% (3.5 GHz to 18 GHz). With the compact, ultra-wideband, and low profile, the proposed antenna can be a very good candidate for a wide range of communication applications. Spider Monkey Optimization (SMO) method is introduced for the first time for solving electromagnetic problems. The SMO is a new swarm intelligence technique which models the foraging behavior of spider monkeys. To show the efficiency of the SMO, different examples are presented and the results are compared with the results obtained using other popular optimization techniques. The optimization procedure is used to synthesis the array factor of a linear antenna array and to optimally design a rectangular and an E-shaped patch antenna for wireless applications. By comparing to traditional optimization techniques that reported in the literature, it is evident that SMO is efficient in reaching the optimum solutions with less number of experiments. The performance results obtained from study of these antennas show that these antennas can be an excellent choice for a wide range of wireless communication applications.