Numerous compact rectangular patch antennas have been designed and developed for UWB and LTE applications. These antennas include hexagonal, octagonal, patch antenna with defected ground structure of Swastik shape, spiral shape patch antenna with partial ground and notch, and slotted- antenna with the partial ground (U - Shaped) for UWB and LTE Applications. In addition to this, the hexagonal and octagonal microstrip patch antennas have been designed with co-planar waveguide feeding method. The parameters such as gain and bandwidth were improved for hexagonal patch antenna when compared to octagonal patch antenna. The rectangular patch antenna has been designed with DGS of Swastik shape and which resulted in bandwidth enhancement for multiband operation and is suitable for LTE applications. Next, the compact spiral shape patch antenna with partial ground and notch has been designed for with partial slotted ground. In this structure, antenna parameters like return loss, VSWR and gain were improved when compared with an antenna without Notch in the ground plane. Similarly, the slotted - patch Antenna with the partial ground (U - shaped) has been designed for LTE applications.