Flexible-antenna systems have recently received significant research interest due to their capability to reconfigure wireless channels intelligently. This paper focuses on a new type of flexible-antenna technology, termed pinching antennas, which can be realized by applying small dielectric particles on a waveguide. Analytical results are first developed for the simple case with a single pinching antenna and a single waveguide, where the unique feature of the pinching-antenna system to create strong line-of-sight links and mitigate large-scale path loss is demonstrated. An advantageous feature of pinching-antenna systems is that multiple pinching antennas can be activated on a single waveguide at no extra cost; however, they must be fed with the same signal. This feature motivates the application of non-orthogonal multiple access (NOMA), and analytical results are provided to demonstrate the superior performance of NOMA-assisted pinching-antenna systems. Finally, the case with multiple pinching antennas and multiple waveguides is studied, which resembles a classical multiple-input single-input (MISO) interference channel. By exploiting the capability of pinching antennas to reconfigure the wireless channel, it is revealed that a performance upper bound on the interference channel becomes achievable, where the achievability conditions are also identified. Computer simulation results are presented to verify the developed analytical results and demonstrate the superior performance of pinching-antenna systems.