This paper presents a comprehensive survey of on-device recommender systems (DeviceRSs), which aim to address the limitations of traditional cloud-based recommender systems (CloudRSs). CloudRSs suffer from high resource consumption, response latency, and privacy and security risks. DeviceRSs leverage edge devices to minimize centralized data storage, reduce communication overhead, and enhance user privacy by processing data locally. The survey covers three main aspects: (1) deployment and inference of DeviceRSs, exploring how large recommendation models can be compressed and utilized within resource-constrained environments; (2) training and update of DeviceRSs, discussing how local data can be leveraged for model optimization; and (3) security and privacy of DeviceRSs, addressing potential vulnerabilities and defensive strategies. The survey provides a systematic taxonomy of methods in each aspect, along with a discussion of challenges and future research directions. It is the first comprehensive survey of DeviceRSs that covers a spectrum of tasks to fit various needs. The survey aims to help readers grasp the current research status, equip them with technical foundations, and stimulate new research ideas for developing DeviceRSs. The survey includes a detailed discussion of various methods for deployment and inference, training and update, and security and privacy, as well as challenges and future directions. The survey is structured into sections covering preliminary concepts, deployment and inference, training and update, and security and privacy. The survey highlights the importance of on-device learning in addressing the limitations of CloudRSs and provides a comprehensive overview of the current state of research in this area.This paper presents a comprehensive survey of on-device recommender systems (DeviceRSs), which aim to address the limitations of traditional cloud-based recommender systems (CloudRSs). CloudRSs suffer from high resource consumption, response latency, and privacy and security risks. DeviceRSs leverage edge devices to minimize centralized data storage, reduce communication overhead, and enhance user privacy by processing data locally. The survey covers three main aspects: (1) deployment and inference of DeviceRSs, exploring how large recommendation models can be compressed and utilized within resource-constrained environments; (2) training and update of DeviceRSs, discussing how local data can be leveraged for model optimization; and (3) security and privacy of DeviceRSs, addressing potential vulnerabilities and defensive strategies. The survey provides a systematic taxonomy of methods in each aspect, along with a discussion of challenges and future research directions. It is the first comprehensive survey of DeviceRSs that covers a spectrum of tasks to fit various needs. The survey aims to help readers grasp the current research status, equip them with technical foundations, and stimulate new research ideas for developing DeviceRSs. The survey includes a detailed discussion of various methods for deployment and inference, training and update, and security and privacy, as well as challenges and future directions. The survey is structured into sections covering preliminary concepts, deployment and inference, training and update, and security and privacy. The survey highlights the importance of on-device learning in addressing the limitations of CloudRSs and provides a comprehensive overview of the current state of research in this area.