This thesis is devoted to potential applications of metamaterials in antenna structures as well as metamaterials behaviour, characterisation, structure design, simulation and extraction of parameters. The focus of this work is on the practical application of metamaterial structures for antenna performance enhancement. This thesis comprises three key parts; In the first part, theory of metamaterials is investigated including fields, polarisation, effective and average parameters, parameters extraction and transmission line (TL) model. In part two, zero index metamaterials (ZIM) theory is studied. The use of ZIM to form a highly directive medium is illustrated. A comparative study between different ZIM structures is conducted with a special attention to their operational bandwidth. ANSYS HFSS is used to model ZIM structures where simulation results show a bandwidth between 7.4% and 14.0%. Then two novel ZIM structures with a bandwidth of up to 33% are proposed. The first proposed ZIM is used to form a highly directive shell. Four directive shells are designed and placed around the dipole antenna where a gain increase of up to 6.8 dBi is obtained along the desired direction. Further, proposed ZIM cells are integrated with a quasi-Yagi antenna in order to increase its gain. Simulation results demonstrate gain enhancement for frequencies over which the proposed structure expresses ZIM properties. In part three, a new technique is stablished to design a metamaterial lens. The new technique is based on wave interference phenomena where engineered wave interference results in a desired spatial energy distribution. It is shown theoretically that having 180° phase difference between interfering waves results in a focused emission. Both hypothetical and metamaterial realisation models of a 180° phase shifter for a patch antenna are designed and simulated where a gain enhancement of 8 dBi and 5.77 dBi are achieved, respectively. Further, the concept of intended phase shift between interfering waves is used to design a novel bi-reflectional ground plane which can focus the reflected emission and consequently, increase the antenna directivity. In the theoretical model, the Perfect-E and Perfect-H planes are combined to form a bi-reflectional plane, whereas the practical model is designed using the copper cladding for the Perfect-E plane and the mushroom structure for the perfect-H plane. Both square and hexagonal geometries are used to form the mushroom structure. Simulation results confirm a gain enhancement of 5.4 dBi for the design using the square mushroom structure and a gain enhancement of 3.3 dBi for the design using the hexagonal mushroom structure.