Pinching antenna systems (PASS) present a breakthrough among the flexible-antenna technologies, and distinguish themselves by facilitating large-scale antenna reconfiguration, line-of-sight creation, scalable implementation, and near-field benefits, thus bringing wireless communications from the last mile to the last meter. A comprehensive tutorial is presented in this paper. First, the fundamentals of PASS are discussed, including PASS signal models, hardware models, power radiation models, and pinching antenna activation methods. Building upon this, the information-theoretic capacity limits achieved by PASS are characterized, and several typical performance metrics of PASS-based communications are analyzed to demonstrate its superiority over conventional antenna technologies. Next, the pinching beamforming design is investigated. The corresponding power scaling law is first characterized. For the joint transmit and pinching design in the general multiple-waveguide case, 1) a pair of transmission strategies is proposed for PASS-based single-user communications to validate the superiority of PASS, namely sub-connected and fully connected structures; and 2) three practical protocols are proposed for facilitating PASS-based multi-user communications, namely waveguide switching, waveguide division, and waveguide multiplexing. A possible implementation of PASS in wideband communications is further highlighted. Moreover, the channel state information acquisition in PASS is elaborated with a pair of promising solutions. To overcome the high complexity and suboptimality inherent in conventional convex-optimization-based approaches, machine-learning-based methods for operating PASS are also explored, focusing on selected deep neural network architectures and training algorithms. Finally, several promising applications of PASS in next-generation wireless networks are highlighted.