Abstract: A periodic structure usually features stopbands. Some stopbands are useful for some leaky-wave antennas. For example, it can be used for suppressing unwanted mode in a leaky-wave antenna. On the other hand, some stopbands are deleterious for most of periodic leaky-wave antennas. For example, the open stopband in a periodic leaky-wave antenna forbids the beam scanning continuously through the broadside direction. This paper discusses the utilization and the suppression of the stopband in leaky-wave antennas. An example for the utilization of stopband is given. The microstrip leaky-wave antenna typically works in the EH1 mode. When exciting the EH1 mode for the leaky-wave antenna, the unwanted EH0 mode is excited. By placing a set of periodic shorting vias along the center line of the antenna, a stopband in the EH0 mode is generated, which can be exploited for the efficient suppression of the propagation of the unwanted EH0 mode. With the suppression of the unwanted EH0 mode, the antenna exhibits a lower reflection coefficient, a higher and more stable realized gain. In addition, three methods are presented for the complete suppression of the undesired open stopband in periodic leaky-wave antennas, i. e. , the unit cell of dual non-identical element, the shorting-via matching, and the tapered half-wavelength transmission line. With the complete suppression of the open stopband, the periodic leaky-wave antennas can have the main beam scanning continuously from the backward to the forward, and therefore the scanning range is greatly enlarged. The methods can be applied to planar and non-planar periodic leaky-wave antennas based on substrate integrated waveguide, microstrip, coaxial line, etc.