The rapid evolution of 5G and beyond technologies has sparked an unprecedented surge in the need for networking infrastructure that can deliver high speed, minimal latency, and remarkable flexibility. The programmable data plane, which enables the dynamic reconfiguration of network functions and protocols, is becoming increasingly important in meeting these requirements. This paper provides an overview of the current state of the art in programmable data planes implemented in 5G and beyond architectures. It proposes a classification of the reviewed studies based on system architecture and specific use cases. Furthermore, the article surveys the primary applications of programmable devices in emerging telecommunication networks, such as tunneling and forwarding, network slicing, cybersecurity, and in-band telemetry. Finally, this publication summarizes the open research challenges and future directions. In addition to offering a comprehensive review of programmable data plane applications in telecommunication networks, this article aims to guide further research in this promising field for network operators and researchers alike.