As the demand for compact, portable communication electronics increases, the technology of miniaturization has made great progress. A beneficiary of that progress has been research into new concepts for the antenna, one of the essential components in wireless communications. As the size of an antenna becomes smaller, however, the antenna suffers from high Q and low radiation resistance. The results are narrow bandwidth, poor matching, low efficiency, and, more generally, poor performance throughout the communication system. First, the design of a small antenna for HF/VHF communications is described. As the operating frequency of an antenna decreases, for example, into the HF and low VHF regions, the physical size of the antenna becomes a critical issue. It is desirable to design a truly electrically small antenna by reducing the ground plane size. Moreover, when the antenna size is very small, the bandwidth of the antenna is extremely narrow, which is critical to various deployment variances and propagation effects such as multi-path fading. The new design, which is an inductively coupled, top-loaded, monopole structure optimized by a genetic algorithm (GA), maximizes transmission of HF/VHF waves. Electrically small, spiral ground planes for the monopole and the electrically small antenna are designed for HF ground-wave transmission. In addition, a tunable small antenna is investigated that overcomes the narrow-bandwidth limitation of electrically small antennas. Second, new design methodologies for electrically small antennas are discussed. Use of an inductively coupled feed is one of the well-known methods for boosting input resistance. As the antenna size becomes smaller, however, it is found that the efficiency of an antenna using an inductively coupled feed is lower than an antenna using multiple folds. After a comparison of the two methods, the design of a thin, multiply folded, electrically small antenna is proposed for achieving high efficiency in a physically compact size. The GA is used to assess the effect of geometry on the performance (in terms of efficiency and bandwidth) of the electrically small antennas, including the folded conical helix and folded spherical helix. Finally, the prospects of using the new Yagi antennas to achieve small size are explored. Yagi antennas are used widely to obtain high gain in a simple structures. The antenna is composed of the driven element and the parasitic elements, which include a reflector and one or more directors. Typically, sufficient spacing on the order of 0.15[lambda] to 0.4[lambda] between the driven element and the parasitic elements is needed for the Yagi antenna to operate well. For some applications, however, it is desirable to reduce the spacing and the length of the elements to achieve a physically more compact size. In this dissertation, closely spaced, folded Yagi antennas in both three dimensions and two dimensions are investigated, and a design for an electrically small Yagi antenna is suggested.