A considerable amount of research has been dedicated to the miniaturization of antennas in recent years. Emerging broadband and mobile wireless applications with market pressure for miniaturized communication devices have encouraged the use of electrically small antennas (ESA). Reduction of antenna size and miniaturization of radiating structures gives rise to some unavoidable limitations on their radiation performance. The need for small portable devices has motivated many engineers and scientists to study these fundamental limits. Physical bounds on the bandwidth, realized gain, directivity, gain-bandwidth product, scattered power, and absorption efficiency have been discussed in this thesis. The concept of antenna quality factor relating the antenna realizable bandwidth to the equivalent current distributions induced over the antenna structure plays an important role in this matter. Numerous papers have been published trying to define the minimum possible radiation quality factor of the antenna as a function of its size. Many of these derivations assume a circumscribing sphere and deal only with the fields external to this sphere. As a result, the lower limits tend to be overly optimistic and the actual quality factor of the antenna is usually considerably higher than the lower bound predicted by these theories. In this thesis a general expression for the quality factor of an arbitrary current distribution is derived based on the concept of observable stored energy. The given expression closely predicts the actual impedance bandwidth of the antenna which is derived from its resonance model. In order to design antennas with optimal radiation performance a novel scheme based on the theory of characteristic modes is developed. The new design methodology is applicable to arbitrary topologies and it does not rely on the assumption of a canonical volume such as a sphere enclosing the antenna. The particular definition of characteristic modes, as proposed in this thesis, substantially reduces the number of basis functions required to expand a realizable current distribution over an arbitrary topology. By developing the novel notion of “generalized Chu’s theorem” it has been shown that only a finite number of eigencurrents contribute in radiation and this considerably reduces numerical calculations in the optimization procedure. Furthermore, a general modal technique is established to design spherical antennas with maximum gain-bandwidth product. In addition to the physical limitation of small antennas, a fundamental limitation on the scattering behavior of receiving antennas has been introduced in this thesis for the first time. Specifically, a lower bound on the total power scattered from a lossless and matched receiving antenna, for a given incident wave, is presented. The vector spherical wave expansion is used to describe the scattering and power absorption mechanisms. Scattering is the main reason behind antenna absorption. This poses a fundamental limit on minimization of antenna scattering. In other words, if we are to extract any power from the incident wave, the receiving antenna cannot be completely invisible and scattering is an inevitable consequence of the power capturing process. Finally, a universal limit on the absorption efficiency of arbitrary receiving antennas in terms of their normalized gain is derived which is based on the modal analysis of the scattering process in receiving mode. Key Words Quality factor, Impedance bandwidth, Characteristic modes, Antenna scattering, Absorption efficiency