Flexible-antenna systems, such as fluid antennas and movable antennas, have been recognized as key enabling technologies for sixth-generation (6G) wireless networks, as they can intelligently reconfigure the effective channel gains of the users and hence significantly improve their data transmission capabilities. However, existing flexible-antenna systems have been designed to combat small-scale fading in non-line-of-sight (NLoS) conditions. As a result, they lack the ability to establish line-of-sight links, which are typically 100 times stronger than NLoS links. In addition, existing flexible-antenna systems have limited flexibility, where adding/removing an antenna is not straightforward. This article introduces an innovative flexible-antenna system called pinching antennas, which are realized by applying small dielectric particles to waveguides. We first describe the basics of pinching-antenna systems and their ability to provide strong LoS links by deploying pinching antennas close to the users as well as their capability to scale up/down the antenna system. We then focus on communication scenarios with different numbers of waveguides and pinching antennas, where innovative approaches to implement multiple-input multiple-output and non-orthogonal multiple access are discussed. In addition, promising 6G-related applications of pinching antennas, including integrated sensing and communication and next-generation multiple access, are presented. Finally, important directions for future research, such as waveguide deployment and channel estimation, are highlighted.